install.packages("dplyr")NB: The dplyr package
The dplyr package was developed by Hadley Wickham of RStudio and is an optimized and distilled version of his plyr package.
Note
plyr is an attempt to organize much of the functionality of the *apply family of methods in base R. Although in many ways superseded the plyr and dplyr, they remain useful.
The dplyr package does not provide any “new” functionality to R per se; everything dplyr does could already be done with base R. But it greatly simplifies existing functionality in R.
One important contribution of the dplyr package is that it provides a “grammar” (in particular, verbs) for data manipulation and for operating on data frames.
With this grammar, you can clearly communicate what it is that you are doing to a data frame that other people can understand (assuming they also know the grammar).
This is useful because it provides an abstraction for data manipulation that previously did not exist within R and other programming languages.
Another useful contribution is that the dplyr functions are very fast, as many key operations are coded in C++.
dplyr Grammar
Some of the key “verbs” provided by the dplyr package are:
select: return a subset of the columns of a data frame, using a flexible notationfilter: extract a subset of rows from a data frame based on logical conditionsarrange: reorder rows of a data framerename: rename variables in a data framemutate: add new variables/columns or transform existing variablessummarise/summarize: generate summary statistics of different variables in the data frame, possibly within strata%>%: the “pipe” operator is used to connect multiple verb actions together into a pipeline
Common dplyr Function Properties
All of the functions that we will discuss in this Chapter will have a few common characteristics. In particular,
The first argument is a data frame.
The subsequent arguments describe what to do with the data frame specified in the first argument, and you can refer to columns in the data frame directly without using the $ operator (just use the column names).
The return result of a function is a new data frame.
Data frames must be properly formatted and annotated for this to all be useful.
In particular, the data must be tidy The main principles of tidy data are:
Each variable forms a column.
Each observation forms a row.
Each type of observational unit forms a table.
Installing the dplyr package
The dplyr package can be installed from CRAN or from GitHub using the devtools package and the install_github() function.
The GitHub repository will usually contain the latest updates to the package and the development version.
To install from CRAN, just run
To install from GitHub you can run
install_github("hadley/dplyr")After installing the package it is important that you load it into your R session with the library() function.
library(dplyr)
Attaching package: 'dplyr'The following objects are masked from 'package:stats':
filter, lagThe following objects are masked from 'package:base':
intersect, setdiff, setequal, unionYou may get some warnings when the package is loaded because there are functions in the dplyr package that have the same name as functions in other packages. For now you can ignore the warnings.
Getting a dataset
Let’s use a dataset containing air pollution and temperature data for the city of Chicago in the U.S.
You will find the data in the directory for this module.
Load the data into R using the readRDS() function.
chicago <- readRDS("chicago.rds")You can see some basic characteristics of the dataset with the dim() and str() functions.
dim(chicago)[1] 6940 8str(chicago)'data.frame': 6940 obs. of 8 variables:
$ city : chr "chic" "chic" "chic" "chic" ...
$ tmpd : num 31.5 33 33 29 32 40 34.5 29 26.5 32.5 ...
$ dptp : num 31.5 29.9 27.4 28.6 28.9 ...
$ date : Date, format: "1987-01-01" "1987-01-02" ...
$ pm25tmean2: num NA NA NA NA NA NA NA NA NA NA ...
$ pm10tmean2: num 34 NA 34.2 47 NA ...
$ o3tmean2 : num 4.25 3.3 3.33 4.38 4.75 ...
$ no2tmean2 : num 20 23.2 23.8 30.4 30.3 ...head(chicago) city tmpd dptp date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 chic 31.5 31.500 1987-01-01 NA 34.00000 4.250000 19.98810
2 chic 33.0 29.875 1987-01-02 NA NA 3.304348 23.19099
3 chic 33.0 27.375 1987-01-03 NA 34.16667 3.333333 23.81548
4 chic 29.0 28.625 1987-01-04 NA 47.00000 4.375000 30.43452
5 chic 32.0 28.875 1987-01-05 NA NA 4.750000 30.33333
6 chic 40.0 35.125 1987-01-06 NA 48.00000 5.833333 25.77233Core Methods
select()
We use the select() function to select columns you want to focus on.
Suppose we wanted to take the first 3 columns only.
There are a few ways to do this.
We could for example use numerical indices.
head(chicago[names(chicago)[1:3]]) city tmpd dptp
1 chic 31.5 31.500
2 chic 33.0 29.875
3 chic 33.0 27.375
4 chic 29.0 28.625
5 chic 32.0 28.875
6 chic 40.0 35.125But we can also use the names directly.
chicago %>%
select(city:dptp) %>%
head(10) city tmpd dptp
1 chic 31.5 31.500
2 chic 33.0 29.875
3 chic 33.0 27.375
4 chic 29.0 28.625
5 chic 32.0 28.875
6 chic 40.0 35.125
7 chic 34.5 26.750
8 chic 29.0 22.000
9 chic 26.5 29.000
10 chic 32.5 27.750Note the use of : inside the select() — you can use it to specify a range of variable names.
You can also omit variables using the select() function by using the negative sign.
With select() you can do:
select(chicago, -(city:dptp)) %>% head(10) date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 1987-01-01 NA 34.00000 4.250000 19.98810
2 1987-01-02 NA NA 3.304348 23.19099
3 1987-01-03 NA 34.16667 3.333333 23.81548
4 1987-01-04 NA 47.00000 4.375000 30.43452
5 1987-01-05 NA NA 4.750000 30.33333
6 1987-01-06 NA 48.00000 5.833333 25.77233
7 1987-01-07 NA 41.00000 9.291667 20.58171
8 1987-01-08 NA 36.00000 11.291667 17.03723
9 1987-01-09 NA 33.28571 4.500000 23.38889
10 1987-01-10 NA NA 4.958333 19.54167This indicates that we should include every variable except the variables city through dptp.
The equivalent code in base R would be
i <- match("city", names(chicago))
j <- match("dptp", names(chicago))
head(chicago[, -(i:j)]) date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 1987-01-01 NA 34.00000 4.250000 19.98810
2 1987-01-02 NA NA 3.304348 23.19099
3 1987-01-03 NA 34.16667 3.333333 23.81548
4 1987-01-04 NA 47.00000 4.375000 30.43452
5 1987-01-05 NA NA 4.750000 30.33333
6 1987-01-06 NA 48.00000 5.833333 25.77233Not super intuitive, right?
The select() function also allows a special syntax that allows you to specify variable names based on patterns.
So, for example, if you wanted to keep every variable that ends with a “2”, we could do
chicago %>%
select(ends_with("2")) %>%
head(10) pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 NA 34.00000 4.250000 19.98810
2 NA NA 3.304348 23.19099
3 NA 34.16667 3.333333 23.81548
4 NA 47.00000 4.375000 30.43452
5 NA NA 4.750000 30.33333
6 NA 48.00000 5.833333 25.77233
7 NA 41.00000 9.291667 20.58171
8 NA 36.00000 11.291667 17.03723
9 NA 33.28571 4.500000 23.38889
10 NA NA 4.958333 19.54167Or if we wanted to keep every variable that starts with a “d”, we could do
chicago %>%
select(starts_with("d")) %>%
head(10) dptp date
1 31.500 1987-01-01
2 29.875 1987-01-02
3 27.375 1987-01-03
4 28.625 1987-01-04
5 28.875 1987-01-05
6 35.125 1987-01-06
7 26.750 1987-01-07
8 22.000 1987-01-08
9 29.000 1987-01-09
10 27.750 1987-01-10This is super useful if you have a table with prefixes, such as doc_.
You can also use more general regular expressions if necessary.
See ?select for more info.
?selectAside: Helper Functions
Note the use the function ends_with() inside of the argument space for the function select() above.
ends_with() is an example of a “helper function” — a function that helps make dplyr functions more effective.
There are many of these introduced by dplyer. Here is a set of helper functions that can be especially useful with select() and related functions to specify variable names based on certain patterns or characteristics:
| Helper Function | Description | Example |
|---|---|---|
starts_with() |
Matches variable names that start with a given prefix | select(data, starts_with("X")) |
ends_with() |
Matches variable names that end with a given suffix | select(data, ends_with("_2019")) |
contains() |
Matches variable names that contain a given string | select(data, contains("income")) |
matches() |
Matches variable names that match a given regular expression | select(data, matches("^X[1-3]$")) |
num_range() |
Matches variable names that match a pattern of prefix + number | select(data, num_range("X", 1:3)) |
one_of() |
Matches variable names that are in a given set of names | select(data, one_of(c("var1", "var2"))) |
everything() |
Matches all variable names (used to reorder variables) | select(data, starts_with("X"), everything()) |
filter()
The filter() function extracts subsets of rows from a data frame.
Note
select() is a column-wise operation, filter() is row-wise.
This function is similar to the existing subset() function in R but is quite a bit faster.
Suppose we wanted to extract the rows of the chicago data frame where the levels of PM2.5 are greater than 30 (which is a reasonably high level), we could do
chicago %>%
filter(pm25tmean2 > 30) %>%
head(10) city tmpd dptp date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 chic 23 21.9 1998-01-17 38.10 32.46154 3.180556 25.30000
2 chic 28 25.8 1998-01-23 33.95 38.69231 1.750000 29.37630
3 chic 55 51.3 1998-04-30 39.40 34.00000 10.786232 25.31310
4 chic 59 53.7 1998-05-01 35.40 28.50000 14.295125 31.42905
5 chic 57 52.0 1998-05-02 33.30 35.00000 20.662879 26.79861
6 chic 57 56.0 1998-05-07 32.10 34.50000 24.270422 33.99167
7 chic 75 65.8 1998-05-15 56.50 91.00000 38.573007 29.03261
8 chic 61 59.0 1998-06-09 33.80 26.00000 17.890810 25.49668
9 chic 73 60.3 1998-07-13 30.30 64.50000 37.018865 37.93056
10 chic 78 67.1 1998-07-14 41.40 75.00000 40.080902 32.59054You can see that there are now only 194 rows in the data frame and the distribution of the pm25tmean2 values is.
summary(chicago$pm25tmean2) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
1.70 9.70 14.66 16.23 20.60 61.50 4447 We can place an arbitrarily complex logical sequence inside of filter(), so we could for example extract the rows where PM2.5 is greater than 30 and temperature is greater than 80 degrees Fahrenheit.
chicago %>%
filter(pm25tmean2 > 30 & tmpd > 80) %>%
select(date, tmpd, pm25tmean2) date tmpd pm25tmean2
1 1998-08-23 81 39.60000
2 1998-09-06 81 31.50000
3 2001-07-20 82 32.30000
4 2001-08-01 84 43.70000
5 2001-08-08 85 38.83750
6 2001-08-09 84 38.20000
7 2002-06-20 82 33.00000
8 2002-06-23 82 42.50000
9 2002-07-08 81 33.10000
10 2002-07-18 82 38.85000
11 2003-06-25 82 33.90000
12 2003-07-04 84 32.90000
13 2005-06-24 86 31.85714
14 2005-06-27 82 51.53750
15 2005-06-28 85 31.20000
16 2005-07-17 84 32.70000
17 2005-08-03 84 37.90000?filterHelp on topic 'filter' was found in the following packages:
Package Library
dplyr /Library/Frameworks/R.framework/Versions/4.0/Resources/library
stats /Library/Frameworks/R.framework/Versions/4.0/Resources/library
Using the first match ...Here’s a table of helper functions specifically associated with filter():
| Helper Function | Description | Example |
|---|---|---|
between() |
Check if a value lies between two other values. | filter(data, between(age, 18, 30)) |
near() |
Check for near equality (useful for floating-point numbers). | filter(data, near(price, 19.99, tolerance = 0.01)) |
isin() (or %in%) |
Check if a value is in a set of values. | filter(data, region %in% c("East", "West")) |
all_of() |
Check for all of the variables, even if some don’t exist. Useful with character vectors. | filter(data, all_of(variables)) |
any_of() |
Check for any of the variables. Useful with character vectors. | filter(data, any_of(variables)) |
cur_group_id() |
Identify the current group inside group_by(). Useful for more complex filtering with groups. |
filter(data, cur_group_id() == 1) |
arrange()
Use arrange() to reorder rows of a data frame according to one or more of the columns.
This normally called sorting, but this word is already used in R.
Reordering rows of a data frame (while preserving corresponding order of other columns) is normally a pain to do in R.
The arrange() function simplifies the process quite a bit.
Here we order the rows of the data frame by date in ascending order:
chicago_by_date <- chicago %>%
arrange(date)
head(chicago_by_date) city tmpd dptp date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 chic 31.5 31.500 1987-01-01 NA 34.00000 4.250000 19.98810
2 chic 33.0 29.875 1987-01-02 NA NA 3.304348 23.19099
3 chic 33.0 27.375 1987-01-03 NA 34.16667 3.333333 23.81548
4 chic 29.0 28.625 1987-01-04 NA 47.00000 4.375000 30.43452
5 chic 32.0 28.875 1987-01-05 NA NA 4.750000 30.33333
6 chic 40.0 35.125 1987-01-06 NA 48.00000 5.833333 25.77233We can now check the first few rows
chicago_by_date %>%
select(date, pm25tmean2) %>%
head(3) date pm25tmean2
1 1987-01-01 NA
2 1987-01-02 NA
3 1987-01-03 NAand the last few rows.
chicago_by_date %>%
select(date, pm25tmean2) %>%
tail(3) date pm25tmean2
6938 2005-12-29 7.45000
6939 2005-12-30 15.05714
6940 2005-12-31 15.00000Columns can be arranged in descending order too by using the special desc() operator.
chicago %>%
arrange(desc(date)) %>%
head() city tmpd dptp date pm25tmean2 pm10tmean2 o3tmean2 no2tmean2
1 chic 35 30.1 2005-12-31 15.00000 23.5 2.531250 13.25000
2 chic 36 31.0 2005-12-30 15.05714 19.2 3.034420 22.80556
3 chic 35 29.4 2005-12-29 7.45000 23.5 6.794837 19.97222
4 chic 37 34.5 2005-12-28 17.75000 27.5 3.260417 19.28563
5 chic 40 33.6 2005-12-27 23.56000 27.0 4.468750 23.50000
6 chic 35 29.6 2005-12-26 8.40000 8.5 14.041667 16.81944Here’s a table of helper functions specifically associated with arrange():
| Helper Function | Description | Example |
|---|---|---|
desc() |
Order by descending instead of default ascending. | arrange(data, desc(salary)) |
across() |
Apply to multiple columns, especially with c_across() in dplyr 1.0.0 and later. |
arrange(data, across(starts_with("X"))) |
row_number() |
Create an index based on the order of rows. | mutate(data, idx = row_number()) |
Note that while row_number() can be used in conjunction with arrange(), it’s often seen in mutate() for creating an index column based on ordering.
The across() function, introduced in dplyr version 1.0.0, provides a more concise syntax for working with multiple columns. It can be especially useful in arrange() when you’re trying to order rows based on a selection of columns that match a certain criterion.
Note that most of the magic with arrange() happens through the way you structure its arguments and not necessarily through a large set of helper functions.
rename()
Renaming a variable in a data frame in R is surprisingly hard to do!
The rename() function is designed to make this process easier.
Here we the names of the first five variables in the chicago data frame.
head(chicago[, 1:5], 3) city tmpd dptp date pm25tmean2
1 chic 31.5 31.500 1987-01-01 NA
2 chic 33.0 29.875 1987-01-02 NA
3 chic 33.0 27.375 1987-01-03 NAThe dptp column is supposed to represent the dew point temperature and the pm25tmean2 column provides the PM2.5 data.
However, these names are awkward and should be renamed to something more sensible.
chicago <- chicago %>%
rename(dewpoint = dptp, pm25 = pm25tmean2)
chicago %>%
head(3) city tmpd dewpoint date pm25 pm10tmean2 o3tmean2 no2tmean2
1 chic 31.5 31.500 1987-01-01 NA 34.00000 4.250000 19.98810
2 chic 33.0 29.875 1987-01-02 NA NA 3.304348 23.19099
3 chic 33.0 27.375 1987-01-03 NA 34.16667 3.333333 23.81548The syntax inside the rename() function is to have the new name on the left-hand side of the = sign and the old name on the right-hand side.
I leave it as an exercise for the reader to figure how you do this in base R without dplyr.
Here’s a table of helper functions that can be used with rename():
| Helper Function | Description | Example |
|---|---|---|
starts_with() |
Match columns that start with a given prefix. | rename(data, start_X = starts_with("X")) (Note: This example would rename the first column that starts with “X” to “start_X”) |
ends_with() |
Match columns that end with a given suffix. | rename(data, end_year = ends_with("_2021")) |
contains() |
Match columns that contain a given string. | rename(data, has_rate = contains("rate")) |
matches() |
Match columns that match a given regular expression. | rename(data, match_num = matches("^X[1-3]$")) |
everything() |
Match all columns. | Rarely used with rename(), but possible. |
It’s worth noting that these helper functions will typically target the first column that meets the specified criterion. If there are multiple columns that match the criterion (e.g., multiple columns that start with “X”), you’ll need to use these helpers with more precision or utilize other techniques.
Also, remember to always refer to the official dplyr documentation as the package continues to evolve and new functionalities might be added over time.
mutate()
The mutate() function creates new columns based on computations usually involving the other columns.
For example, with air pollution data, we often want to de-trend the data by subtracting the mean from the data.
That way we can look at whether a given day’s air pollution level is higher than or less than average (as opposed to looking at its absolute level).
Here we create a pm25detrend variable that subtracts the mean from the pm25 variable.
chicago <- chicago %>%
mutate(pm25detrend = pm25 - mean(pm25, na.rm = TRUE))
chicago %>%
head() city tmpd dewpoint date pm25 pm10tmean2 o3tmean2 no2tmean2 pm25detrend
1 chic 31.5 31.500 1987-01-01 NA 34.00000 4.250000 19.98810 NA
2 chic 33.0 29.875 1987-01-02 NA NA 3.304348 23.19099 NA
3 chic 33.0 27.375 1987-01-03 NA 34.16667 3.333333 23.81548 NA
4 chic 29.0 28.625 1987-01-04 NA 47.00000 4.375000 30.43452 NA
5 chic 32.0 28.875 1987-01-05 NA NA 4.750000 30.33333 NA
6 chic 40.0 35.125 1987-01-06 NA 48.00000 5.833333 25.77233 NAThere is also the related transmute() function, which does the same thing as mutate() but then drops all non-transformed variables.
Here we detrend the PM10 and ozone (O3) variables.
chicago %>%
transmute(pm10detrend = pm10tmean2 - mean(pm10tmean2, na.rm = TRUE),
o3detrend = o3tmean2 - mean(o3tmean2, na.rm = TRUE)) pm10detrend o3detrend
1 0.10479387 -1.518551e+01
2 NA -1.613117e+01
3 0.27146054 -1.610218e+01
4 13.10479387 -1.506051e+01
5 NA -1.468551e+01
6 14.10479387 -1.360218e+01
7 7.10479387 -1.014385e+01
8 2.10479387 -8.143846e+00
9 -0.60949184 -1.493551e+01
10 NA -1.447718e+01
11 -11.89520613 -1.893846e+00
12 -7.89520613 -1.143551e+01
13 19.10479387 -1.447718e+01
14 9.10479387 -1.522718e+01
15 -5.06187279 -1.497718e+01
16 -14.89520613 -1.151885e+01
17 NA -1.360218e+01
18 5.10479387 -1.306051e+01
19 -1.89520613 -4.560513e+00
20 4.10479387 -1.218551e+01
21 -1.03806327 -1.052247e+01
22 18.10479387 -8.935513e+00
23 21.10479387 -4.810513e+00
24 4.10479387 -9.352180e+00
25 NA -1.276885e+01
26 37.10479387 -1.485218e+01
27 5.43812721 -1.343551e+01
28 13.10479387 -1.256051e+01
29 1.10479387 -1.651885e+01
30 25.10479387 -1.064385e+01
31 2.10479387 -9.060513e+00
32 NA -1.139385e+01
33 7.27146054 -1.339385e+01
34 25.10479387 -1.139385e+01
35 3.10479387 -8.935513e+00
36 36.10479387 -1.370635e+01
37 29.10479387 -1.302066e+01
38 10.10479387 -1.368551e+01
39 -15.64520613 5.501987e+00
40 8.10479387 -1.022718e+01
41 2.10479387 -1.112301e+01
42 49.10479387 -1.131397e+01
43 50.10479387 -1.174801e+01
44 5.10479387 -9.065948e+00
45 -9.03806327 -8.268846e+00
46 -21.89520613 8.668654e+00
47 -19.89520613 4.751987e+00
48 -10.89520613 5.501987e+00
49 -6.89520613 4.734777e+00
50 15.10479387 -3.933701e+00
51 35.96193673 -1.093551e+01
52 25.10479387 -1.485218e+01
53 12.10479387 -8.602180e+00
54 13.10479387 -6.393846e+00
55 14.10479387 -6.206346e+00
56 14.10479387 -2.310513e+00
57 -4.89520613 -3.435513e+00
58 22.10479387 -5.227180e+00
59 -2.89520613 -1.256051e+01
60 -18.89520613 -3.814680e+00
61 2.10479387 1.376987e+00
62 -1.89520613 3.144870e-01
63 5.53336530 -1.393551e+01
64 -3.89520613 -5.852180e+00
65 42.10479387 -1.035943e+01
66 15.10479387 5.981154e+00
67 27.10479387 1.173115e+01
68 -8.89520613 1.039782e+01
69 -14.32377755 8.939487e+00
70 4.10479387 3.353204e-01
71 38.10479387 1.001987e+00
72 13.10479387 3.043654e+00
73 15.10479387 -1.706346e+00
74 NA 1.746032e+01
75 -6.89520613 1.693677e+01
76 21.10479387 8.376987e+00
77 29.10479387 -7.688463e-01
78 -1.89520613 1.224008e+01
79 -5.89520613 1.718949e+01
80 6.10479387 1.877282e+01
81 3.96193673 1.823115e+01
82 36.10479387 1.201865e+01
83 24.10479387 6.189487e+00
84 -19.89520613 -4.560513e+00
85 9.10479387 -4.318089e+00
86 13.10479387 -2.998013e+00
87 0.60479387 6.686537e-01
88 3.10479387 1.536709e+00
89 -6.89520613 1.100199e+01
90 9.10479387 4.609359e+00
91 2.10479387 2.017612e+00
92 10.10479387 3.130837e+00
93 -11.46663470 -2.565721e+00
94 -7.89520613 8.955112e+00
95 -15.89520613 1.659574e+01
96 -14.89520613 1.236657e+01
97 -5.89520613 6.059279e+00
98 -14.89520613 1.574904e+00
99 44.39050816 -4.034471e+00
100 35.10479387 2.423862e+00
101 -9.89520613 9.538445e+00
102 3.10479387 6.243058e+00
103 13.10479387 -1.667656e+00
104 -0.89520613 -6.191465e+00
105 -3.89520613 -2.292656e+00
106 -5.89520613 2.671630e+00
107 9.10479387 -1.259892e-01
108 72.10479387 1.209425e+01
109 NA 1.340377e+01
110 21.10479387 2.195511e+01
111 2.30479387 1.033237e+00
112 -5.89520613 -1.035739e+01
113 -7.89520613 -9.340857e+00
114 -17.89520613 8.137404e+00
115 -3.89520613 8.626987e+00
116 24.10479387 1.371032e+01
117 3.43812721 1.649209e+01
118 38.10479387 3.210320e+00
119 27.10479387 1.541676e+01
120 -14.89520613 1.605407e+01
121 32.10479387 1.260812e-01
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1137 -10.52020613 -6.935513e+00
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1199 -1.89520613 -3.250989e+00
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1201 3.10479387 5.260916e+00
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1204 -3.89520613 2.361330e+00
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1210 7.60479387 9.939487e+00
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1261 -6.89520613 1.283441e+01
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1267 -1.89520613 2.085320e+00
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1270 -5.39520613 -4.563463e-01
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1273 8.10479387 1.049831e+01
1274 9.10479387 1.129365e+01
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1278 -15.89520613 1.278029e+00
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1295 13.10479387 6.944815e+00
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1298 -9.89520613 4.188743e+00
1299 -18.52020613 9.939487e+00
1300 2.60479387 7.755789e-01
1301 14.10479387 -8.157213e-01
1302 3.60479387 5.447607e+00
1303 17.10479387 1.182653e+01
1304 40.10479387 2.810615e+01
1305 53.85479387 3.164782e+01
1306 21.10479387 1.372074e+01
1307 -10.89520613 -8.596201e-01
1308 -19.39520613 -5.299423e-01
1309 8.10479387 3.695439e+00
1310 4.10479387 1.172669e+01
1311 32.10479387 1.883416e+01
1312 -14.89520613 9.460320e+00
1313 -20.89520613 6.096259e-01
1314 -24.39520613 -2.068325e+00
1315 4.10479387 3.182749e-01
1316 14.60479387 2.013504e+00
1317 21.96193673 1.435615e+01
1318 11.10479387 1.871032e+01
1319 26.60479387 2.871032e+01
1320 -4.89520613 1.179365e+01
1321 -13.39520613 -2.239456e+00
1322 -7.89520613 -2.252089e+00
1323 20.39050816 8.975201e+00
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1325 6.60479387 -4.352180e+00
1326 -8.89520613 1.572595e+01
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1328 -17.89520613 -7.294888e+00
1329 -15.39520613 -9.602180e+00
1330 -12.39520613 5.495905e+00
1331 5.10479387 4.716208e+00
1332 -5.89520613 6.482512e+00
1333 16.10479387 1.031426e+01
1334 48.10479387 2.268353e+01
1335 56.39050816 1.687427e+01
1336 19.60479387 1.396925e+01
1337 2.10479387 1.005087e+01
1338 -8.39520613 2.148115e+01
1339 24.10479387 3.120338e+01
1340 30.10479387 2.044470e+01
1341 0.27146054 4.805558e+00
1342 -10.39520613 3.421630e+00
1343 50.10479387 9.129963e+00
1344 18.10479387 1.145734e+01
1345 22.60479387 1.123830e+01
1346 -20.39520613 9.142612e+00
1347 7.10479387 3.092787e-01
1348 9.10479387 3.262404e+00
1349 35.10479387 1.673810e+01
1350 24.60479387 1.093677e+01
1351 60.10479387 8.945556e+00
1352 35.60479387 5.703527e+00
1353 4.72979387 -4.149055e+00
1354 -10.39520613 -4.138638e+00
1355 -23.39520613 9.290704e-01
1356 -14.89520613 -1.685513e+00
1357 -16.89520613 -7.539340e+00
1358 -5.89520613 -1.392888e+01
1359 3.53336530 -2.153295e+00
1360 -7.89520613 -8.881942e+00
1361 -12.89520613 -1.038789e+01
1362 -16.39520613 -4.108132e+00
1363 0.10479387 -2.537554e+00
1364 8.10479387 1.528773e+00
1365 12.97979387 -4.756942e+00
1366 11.60479387 1.652364e-01
1367 14.10479387 -1.253922e+00
1368 -21.39520613 -4.161703e+00
1369 -16.89520613 -7.691465e+00
1370 9.60479387 -9.955441e+00
1371 13.85479387 -3.968380e+00
1372 -5.39520613 2.221319e+00
1373 -1.89520613 -9.167656e+00
1374 -4.89520613 4.909725e+00
1375 5.10479387 1.551092e+01
1376 -28.39520613 8.025823e-01
1377 -25.89520613 -6.411703e+00
1378 NA 6.928514e-01
1379 -23.89520613 -8.191465e+00
1380 12.60479387 -1.001386e+01
1381 31.10479387 -9.809219e+00
1382 16.60479387 -4.596227e+00
1383 -8.03806327 -1.114084e+00
1384 -3.39520613 -1.441596e+01
1385 -6.89520613 -6.191465e+00
1386 11.10479387 1.523711e+01
1387 -17.39520613 -5.875989e+00
1388 -12.89520613 -1.150694e+01
1389 -7.27020613 -5.560513e+00
1390 -8.89520613 -3.881942e+00
1391 13.10479387 -1.103075e+01
1392 15.10479387 -1.270121e+01
1393 2.10479387 -1.037418e+01
1394 -11.89520613 -9.655751e+00
1395 11.72979387 -1.320415e+01
1396 17.10479387 -5.798608e+00
1397 -16.89520613 -6.518846e+00
1398 -4.39520613 -1.172123e+01
1399 24.10479387 -2.668173e+00
1400 29.60479387 -9.149799e+00
1401 26.53336530 3.606154e+00
1402 15.60479387 7.106154e+00
1403 10.10479387 -2.271796e-01
1404 -29.89520613 2.311537e-01
1405 -24.89520613 -3.102180e+00
1406 -9.89520613 -1.418551e+01
1407 -7.18092041 -9.143846e+00
1408 -0.39520613 -1.610218e+01
1409 -4.89520613 -1.731051e+01
1410 -6.89520613 -1.168551e+01
1411 -13.89520613 -1.231051e+01
1412 NA -9.477180e+00
1413 9.35479387 -1.160218e+01
1414 6.60479387 -1.351885e+01
1415 13.10479387 6.606154e+00
1416 4.10479387 -6.060513e+00
1417 -8.89520613 -9.227180e+00
1418 -2.89520613 -1.131051e+01
1419 24.67622245 -1.635218e+01
1420 14.10479387 -1.322718e+01
1421 1.10479387 -8.393846e+00
1422 -6.39520613 -1.126885e+01
1423 -15.89520613 -4.018846e+00
1424 NA -1.560218e+01
1425 -7.27020613 -7.477180e+00
1426 NA -1.143551e+01
1427 -21.89520613 -1.293551e+01
1428 -16.89520613 -1.048097e+01
1429 -2.89520613 -1.418551e+01
1430 -12.39520613 -9.810513e+00
1431 -14.89520613 -1.060218e+01
1432 -19.89520613 -1.855130e-01
1433 -9.89520613 -4.560513e+00
1434 -9.89520613 -7.271796e-01
1435 -6.89520613 -1.389385e+01
1436 -3.39520613 -1.131051e+01
1437 -5.03806327 -1.521812e+01
1438 -1.39520613 -1.568551e+01
1439 -5.89520613 -1.301885e+01
1440 -9.39520613 -8.018846e+00
1441 -0.89520613 -1.147899e+01
1442 1.10479387 -5.141395e+00
1443 -17.32377755 -4.227180e+00
1444 -14.39520613 -8.218122e+00
1445 -15.89520613 -1.543551e+01
1446 -11.39520613 -7.685513e+00
1447 -17.89520613 -1.631051e+01
1448 -9.39520613 -1.406051e+01
1449 -5.56187279 -1.293551e+01
1450 -8.89520613 -1.276885e+01
1451 -4.39520613 -1.601885e+01
1452 -9.89520613 -9.602180e+00
1453 6.10479387 -2.018846e+00
1454 NA -5.018846e+00
1455 -13.46663470 -5.560513e+00
1456 NA -7.602180e+00
1457 -15.89520613 -7.977180e+00
1458 -5.89520613 -1.664385e+01
1459 -21.39520613 -1.581051e+01
1460 NA -7.331346e+00
1461 -7.64520613 -7.662229e+00
1462 NA -8.358590e+00
1463 NA -9.560513e+00
1464 NA -1.018551e+01
1465 9.10479387 -1.256051e+01
1466 NA -1.547718e+01
1467 -6.89520613 -4.810513e+00
1468 NA 2.564487e+00
1469 -5.39520613 -8.143846e+00
1470 3.10479387 -1.464385e+01
1471 1.60479387 -9.310513e+00
1472 -9.89520613 -1.081051e+01
1473 -10.89520613 -1.026885e+01
1474 -0.89520613 -8.727180e+00
1475 10.60479387 -1.172718e+01
1476 12.10479387 -1.476885e+01
1477 -2.39520613 -8.477180e+00
1478 0.10479387 -7.102180e+00
1479 -0.46663470 -1.001885e+01
1480 -14.89520613 -4.935513e+00
1481 -8.89520613 -6.438463e-01
1482 -6.89520613 8.561537e-01
1483 21.10479387 -1.156051e+01
1484 0.10479387 -5.268846e+00
1485 0.85479387 -5.518846e+00
1486 21.10479387 -9.518846e+00
1487 7.10479387 -6.893846e+00
1488 -8.89520613 -6.727180e+00
1489 20.10479387 -7.227180e+00
1490 -21.89520613 9.811537e-01
1491 8.22979387 -7.477180e+00
1492 6.10479387 -4.768846e+00
1493 18.60479387 -1.151885e+01
1494 NA -7.393846e+00
1495 5.10479387 -2.768846e+00
1496 -1.89520613 -6.852180e+00
1497 13.35479387 -6.393846e+00
1498 5.10479387 -4.102180e+00
1499 -5.89520613 -1.110218e+01
1500 8.10479387 -1.285218e+01
1501 1.60479387 -1.060218e+01
1502 -0.89520613 -1.018846e+00
1503 -9.89520613 -1.060513e+00
1504 1.10479387 -1.143551e+01
1505 3.10479387 -1.097718e+01
1506 1.10479387 -3.352180e+00
1507 5.60479387 2.731154e+00
1508 -10.89520613 -6.852180e+00
1509 -4.52020613 -3.935513e+00
1510 5.10479387 -1.114385e+01
1511 NA -8.560513e+00
1512 2.60479387 -3.060513e+00
1513 12.10479387 -8.768846e+00
1514 -6.89520613 -3.521796e-01
1515 -11.02020613 1.397820e+00
1516 -7.89520613 -4.477180e+00
1517 -8.89520613 -2.018846e+00
1518 7.10479387 -5.477180e+00
1519 3.10479387 -4.685513e+00
1520 6.10479387 -6.102180e+00
1521 -4.32377755 2.064487e+00
1522 -7.89520613 -2.060513e+00
1523 -18.89520613 1.939487e+00
1524 -3.89520613 -8.768846e+00
1525 19.10479387 -1.256051e+01
1526 1.10479387 -4.268846e+00
1527 -11.75234898 -1.852180e+00
1528 NA -7.227180e+00
1529 4.60479387 -7.271796e-01
1530 6.10479387 8.978204e-01
1531 23.60479387 -1.477180e+00
1532 -0.89520613 -3.227180e+00
1533 -18.89520613 6.231154e+00
1534 -22.89520613 7.314487e+00
1535 -8.89520613 -2.435513e+00
1536 -7.89520613 3.064487e+00
1537 -0.39520613 -8.935513e+00
1538 17.10479387 -4.362143e+00
1539 9.81907959 -6.518846e+00
1540 -0.89520613 -7.833391e-01
1541 29.10479387 5.607965e+00
1542 -16.89520613 -1.018846e+00
1543 -12.89520613 1.981154e+00
1544 -12.89520613 -1.685513e+00
1545 6.67622245 -1.006051e+01
1546 -2.89520613 2.679624e+00
1547 38.10479387 -3.749005e+00
1548 -5.89520613 5.222028e+00
1549 -19.39520613 9.085320e+00
1550 -12.89520613 6.147820e+00
1551 -7.60949184 4.046673e+00
1552 NA 4.282105e+00
1553 -5.89520613 3.902731e-01
1554 14.10479387 -1.471227e+00
1555 1.10479387 -4.366635e+00
1556 7.10479387 5.738304e+00
1557 -0.14520613 1.922934e+01
1558 -5.89520613 6.814487e+00
1559 10.60479387 -4.022832e+00
1560 -20.89520613 -8.957462e+00
1561 -15.89520613 9.142612e+00
1562 -18.89520613 3.945148e+00
1563 -6.60949184 2.540356e-01
1564 -8.89520613 -6.471227e+00
1565 -21.39520613 -1.054561e+00
1566 -6.89520613 7.156878e+00
1567 NA 2.739026e-01
1568 -16.89520613 1.232777e+00
1569 -3.89520613 6.135374e+00
1570 -11.89520613 6.539125e+00
1571 -19.89520613 1.117758e+01
1572 -18.89520613 1.093121e+01
1573 11.60479387 3.632514e+00
1574 -1.89520613 5.969546e-01
1575 1.47979387 -1.203370e+00
1576 NA 6.635916e+00
1577 38.60479387 8.405937e+00
1578 6.10479387 -7.430305e+00
1579 2.10479387 -4.288774e+00
1580 -13.89520613 1.207344e+00
1581 2.96193673 5.015574e+00
1582 8.10479387 1.731412e+00
1583 25.60479387 6.201933e+00
1584 -24.89520613 2.029290e+00
1585 -4.39520613 -2.840275e+00
1586 -7.89520613 5.704394e-01
1587 -11.77020613 -2.642207e-02
1588 -6.89520613 6.612106e+00
1589 13.10479387 -3.700368e-01
1590 12.10479387 1.089782e+01
1591 37.10479387 9.970261e+00
1592 25.10479387 1.187401e+01
1593 11.10479387 9.195439e+00
1594 46.10479387 1.272412e+01
1595 36.10479387 3.514021e+00
1596 51.10479387 1.569395e+01
1597 54.60479387 3.262404e+00
1598 -1.89520613 -3.285418e+00
1599 -9.52020613 -1.441465e+00
1600 -17.89520613 9.374011e+00
1601 8.10479387 1.030983e+01
1602 59.10479387 1.571458e+01
1603 29.10479387 -6.126410e+00
1604 3.10479387 -1.324718e+00
1605 0.81907959 8.574904e+00
1606 -7.89520613 -4.338166e+00
1607 -4.39520613 9.115729e+00
1608 NA 1.341568e+01
1609 64.10479387 8.586097e+00
1610 10.10479387 9.918654e+00
1611 2.72979387 1.102441e+01
1612 14.10479387 6.529387e+00
1613 7.10479387 1.458532e+01
1614 14.10479387 1.902877e+01
1615 -2.39520613 1.616960e+01
1616 -17.89520613 1.262695e+01
1617 -11.32377755 6.393806e+00
1618 -7.89520613 7.815619e+00
1619 11.10479387 9.600945e+00
1620 14.10479387 1.436136e+01
1621 25.60479387 2.867907e+01
1622 52.10479387 2.323115e+01
1623 4.22979387 6.304070e+00
1624 -8.89520613 3.142612e+00
1625 18.60479387 2.229796e+01
1626 8.10479387 2.333011e+01
1627 -0.39520613 1.869990e+01
1628 -12.89520613 1.363265e+01
1629 -3.39520613 8.779840e+00
1630 -0.89520613 2.567386e+01
1631 9.10479387 3.247074e+01
1632 26.10479387 4.366865e+01
1633 51.10479387 2.639782e+01
1634 -15.89520613 2.025945e+00
1635 -17.27020613 1.245511e+01
1636 -0.89520613 2.086068e+01
1637 18.60479387 3.443564e+01
1638 62.10479387 3.024261e+01
1639 61.10479387 2.925199e+01
1640 15.10479387 2.365303e+01
1641 17.60479387 2.347595e+01
1642 NA 1.472595e+01
1643 35.10479387 1.234884e+01
1644 0.10479387 1.192080e+01
1645 27.60479387 4.703300e+00
1646 NA 5.557920e+00
1647 1.72979387 1.195511e+01
1648 -1.89520613 2.117386e+01
1649 3.60479387 2.024157e+01
1650 NA 1.151082e+01
1651 4.10479387 4.532331e+00
1652 -11.89520613 1.605928e+01
1653 10.60479387 2.278052e+01
1654 24.10479387 1.527622e+01
1655 -11.39520613 1.242907e+01
1656 NA 5.538445e+00
1657 16.60479387 1.161657e+01
1658 23.10479387 2.110095e+01
1659 49.10479387 3.096032e+01
1660 42.10479387 3.347595e+01
1661 51.60479387 3.860999e+01
1662 15.10479387 3.335020e+01
1663 20.10479387 2.883579e+01
1664 36.10479387 1.542229e+01
1665 -3.89520613 1.163877e+01
1666 17.10479387 6.084188e+00
1667 -17.89520613 3.817091e+00
1668 -9.39520613 5.013892e+00
1669 -15.39520613 1.010568e+01
1670 NA 2.221553e+01
1671 4.47979387 1.555060e+01
1672 -6.89520613 6.735783e+00
1673 30.60479387 1.618521e+01
1674 NA 1.489782e+01
1675 97.10479387 2.008301e+01
1676 -18.89520613 1.132375e+01
1677 -19.60949184 3.013561e+00
1678 NA 8.425177e+00
1679 5.60479387 1.193949e+01
1680 8.10479387 6.893191e+00
1681 -1.39520613 8.279798e+00
1682 -18.89520613 9.823142e+00
1683 -9.39520613 4.008511e+00
1684 -5.89520613 8.745043e+00
1685 2.60479387 5.083006e+00
1686 -2.89520613 8.523533e+00
1687 31.10479387 9.359942e+00
1688 29.10479387 1.151578e+01
1689 24.60479387 1.452745e+01
1690 1.10479387 1.119412e+01
1691 0.60479387 6.587635e+00
1692 -15.89520613 -1.915311e+00
1693 -8.39520613 -6.827352e-01
1694 14.10479387 3.273626e+00
1695 8.10479387 1.215708e+01
1696 -15.89520613 3.136512e+00
1697 9.60479387 2.086596e+01
1698 28.10479387 3.335092e+01
1699 46.60479387 2.361568e+01
1700 8.10479387 8.591603e+00
1701 35.96193673 1.232838e+01
1702 39.10479387 1.189782e+01
1703 13.60479387 -2.463291e+00
1704 -4.89520613 1.970737e+00
1705 -9.39520613 1.051240e+01
1706 NA 1.168353e+01
1707 0.85479387 -3.971971e+00
1708 -20.89520613 1.897216e+00
1709 28.10479387 -2.129980e-01
1710 -14.89520613 5.100945e+00
1711 29.60479387 1.164374e+01
1712 7.10479387 1.857490e+01
1713 16.72979387 7.319695e+00
1714 -18.89520613 1.251987e+00
1715 -12.89520613 -1.207289e+00
1716 0.10479387 7.777204e-02
1717 19.60479387 5.163445e+00
1718 -0.89520613 -1.982388e+00
1719 0.39050816 2.778029e+00
1720 9.10479387 -1.315721e+00
1721 6.60479387 -8.055305e+00
1722 8.10479387 -5.473104e+00
1723 4.10479387 -6.805883e+00
1724 -5.89520613 -7.568889e+00
1725 0.10479387 1.894870e-01
1726 -8.89520613 -7.093225e-01
1727 -1.89520613 -9.686097e+00
1728 -5.89520613 -1.376905e+01
1729 2.10479387 -1.130327e+01
1730 6.10479387 -8.307896e+00
1731 -0.27020613 -1.049696e+01
1732 -17.89520613 -4.069772e+00
1733 -1.89520613 1.064487e+00
1734 42.10479387 7.202715e+00
1735 26.10479387 -3.501133e+00
1736 13.10479387 2.074764e-01
1737 -2.52020613 -2.810780e+00
1738 -18.89520613 -4.070930e+00
1739 -14.89520613 -2.643846e+00
1740 -17.89520613 -9.039680e+00
1741 -5.39520613 -1.097797e+01
1742 -4.89520613 3.479946e+00
1743 17.53336530 -2.276093e+00
1744 29.10479387 -5.413095e+00
1745 4.10479387 -8.120698e+00
1746 -8.89520613 -5.079031e+00
1747 -16.39520613 -6.278106e+00
1748 NA -1.333366e+01
1749 -6.27020613 -1.345445e+01
1750 3.10479387 -9.643846e+00
1751 44.60479387 -4.249523e+00
1752 -7.89520613 -4.436776e+00
1753 -6.39520613 -6.139217e+00
1754 -13.89520613 -7.551254e+00
1755 12.10479387 -4.541994e+00
1756 12.10479387 5.512051e+00
1757 27.60479387 -4.236582e-02
1758 -8.89520613 -1.017028e+01
1759 -17.89520613 -1.370114e+01
1760 -13.89520613 -1.037301e+01
1761 -23.89520613 -1.140426e+01
1762 -31.89520613 -1.201885e+01
1763 5.10479387 -1.423239e+01
1764 -25.89520613 -1.366795e+01
1765 NA -1.167956e+01
1766 NA -9.143846e+00
1767 -10.89520613 -6.646796e-01
1768 -16.89520613 -3.373013e+00
1769 11.60479387 -7.956346e+00
1770 -7.89520613 -1.408859e+01
1771 1.10479387 -7.914680e+00
1772 -3.89520613 -1.297718e+01
1773 5.35479387 -1.441468e+01
1774 -26.89520613 -1.296825e+01
1775 11.10479387 -1.601885e+01
1776 NA -1.726885e+01
1777 5.60479387 -1.656051e+01
1778 -5.89520613 -1.558135e+01
1779 2.10479387 -1.556051e+01
1780 4.10479387 -1.001885e+01
1781 -5.39520613 -1.646796e-01
1782 NA -7.143846e+00
1783 2.10479387 -1.064385e+01
1784 -5.89520613 -1.022718e+01
1785 -12.02020613 -1.389385e+01
1786 NA -1.524801e+01
1787 11.60479387 -1.710218e+01
1788 -13.89520613 -1.318551e+01
1789 -0.89520613 -4.331346e+00
1790 -6.89520613 -1.300694e+01
1791 3.47979387 -1.587301e+01
1792 1.10479387 -1.271088e+01
1793 -23.89520613 -7.706346e+00
1794 NA -8.706346e+00
1795 -14.89520613 -5.435513e+00
1796 -14.89520613 -1.353968e+01
1797 -17.27020613 -8.081346e+00
1798 -11.89520613 -1.099801e+01
1799 1.10479387 -1.128968e+01
1800 -10.89520613 -1.422084e+01
1801 -0.39520613 -1.385218e+01
1802 -13.89520613 -1.456051e+01
1803 -9.60949184 -1.316468e+01
1804 8.10479387 -1.543551e+01
1805 -8.39520613 -1.612301e+01
1806 -5.89520613 -1.599801e+01
1807 -6.89520613 -1.558135e+01
1808 7.10479387 -1.656051e+01
1809 2.85479387 -5.602180e+00
1810 -7.89520613 -7.373013e+00
1811 -6.39520613 -1.458135e+01
1812 12.10479387 -1.191468e+01
1813 -2.89520613 -1.068551e+01
1814 3.10479387 -1.562301e+01
1815 -4.52020613 -1.731051e+01
1816 -13.89520613 -1.743551e+01
1817 -22.39520613 -1.618551e+01
1818 -11.89520613 -1.314385e+01
1819 -4.89520613 -1.489385e+01
1820 5.10479387 -1.612301e+01
1821 -0.89520613 -1.533135e+01
1822 -2.89520613 -1.024801e+01
1823 -6.89520613 -1.199801e+01
1824 8.10479387 -1.570635e+01
1825 -4.89520613 -1.438968e+01
1826 -12.89520613 -1.333859e+01
1827 -0.46663470 -1.397718e+01
1828 -2.89520613 -1.701885e+01
1829 -1.89520613 -1.731051e+01
1830 -11.89520613 -1.331051e+01
1831 -8.39520613 -1.143551e+01
1832 -3.89520613 -1.639385e+01
1833 7.53336530 -1.695635e+01
1834 -7.39520613 -1.606051e+01
1835 -0.39520613 -1.743551e+01
1836 -1.89520613 -1.495725e+01
1837 -8.89520613 -1.445635e+01
1838 -10.89520613 -1.201885e+01
1839 -15.77020613 -1.266468e+01
1840 -9.89520613 -7.873013e+00
1841 4.10479387 -1.118362e+01
1842 5.10479387 -1.162112e+01
1843 0.60479387 -8.268846e+00
1844 NA -7.810513e+00
1845 -6.39520613 -1.220635e+01
1846 8.10479387 -1.310218e+01
1847 10.10479387 -1.493551e+01
1848 0.10479387 -1.510218e+01
1849 16.10479387 -1.084027e+01
1850 31.10479387 -7.539680e+00
1851 -9.14520613 -1.220635e+01
1852 -4.89520613 -1.166468e+01
1853 11.60479387 -1.572718e+01
1854 7.10479387 -1.401885e+01
1855 12.60479387 -1.324801e+01
1856 6.60479387 -1.714385e+01
1857 -13.77020613 -9.581346e+00
1858 7.60479387 -3.123013e+00
1859 -10.39520613 -1.501885e+01
1860 48.60479387 -1.685218e+01
1861 -7.39520613 -1.026885e+01
1862 -10.89520613 -1.145635e+01
1863 3.10479387 -1.401885e+01
1864 0.60479387 -8.706346e+00
1865 -8.89520613 -6.206346e+00
1866 9.60479387 -1.191468e+01
1867 44.10479387 -1.622718e+01
1868 -14.89520613 -8.914680e+00
1869 -2.52020613 -5.539680e+00
1870 3.60479387 -1.722718e+01
1871 -2.39520613 -1.307301e+01
1872 -8.39520613 -1.572718e+01
1873 -7.89520613 -1.243551e+01
1874 2.10479387 -9.977180e+00
1875 3.96193673 -1.573760e+01
1876 -7.89520613 -1.375172e+01
1877 3.10479387 -9.554561e+00
1878 -8.89520613 -4.687407e+00
1879 -3.89520613 -8.602180e+00
1880 1.10479387 -1.768846e+00
1881 4.22979387 -8.956346e+00
1882 2.60479387 -8.130589e+00
1883 2.10479387 -5.956346e+00
1884 0.10479387 -1.145824e+01
1885 -6.89520613 -5.977180e+00
1886 -11.89520613 3.272820e+00
1887 2.47979387 -1.018846e+00
1888 10.60479387 -8.081346e+00
1889 25.10479387 -1.253968e+01
1890 43.10479387 -1.068551e+01
1891 65.10479387 -1.260218e+01
1892 16.10479387 -1.131051e+01
1893 9.81907959 -1.589385e+01
1894 -6.39520613 -1.043551e+01
1895 0.10479387 -4.977180e+00
1896 -1.39520613 3.585320e+00
1897 0.10479387 1.751987e+00
1898 -2.39520613 -1.352180e+00
1899 -0.14520613 -1.685513e+00
1900 -6.89520613 3.561537e-01
1901 -5.39520613 -4.980130e-01
1902 -5.39520613 -7.238543e+00
1903 -7.39520613 1.897820e+00
1904 -13.39520613 7.106154e+00
1905 -9.89520613 9.327168e+00
1906 6.10479387 -3.602180e+00
1907 -0.89520613 1.010615e+01
1908 -14.39520613 6.085320e+00
1909 20.10479387 -5.998013e+00
1910 24.10479387 -2.839680e+00
1911 6.85479387 -7.248013e+00
1912 12.60479387 -3.602180e+00
1913 -7.39520613 4.397820e+00
1914 5.60479387 -1.414680e+00
1915 -8.89520613 7.835320e+00
1916 0.10479387 1.043654e+00
1917 1.47979387 -2.768846e+00
1918 -13.89520613 3.789834e+00
1919 -1.89520613 -9.193417e-01
1920 11.60479387 -5.945930e+00
1921 -13.89520613 7.501987e+00
1922 -4.89520613 1.470737e+00
1923 8.22979387 -1.591763e+00
1924 42.60479387 -4.939301e+00
1925 19.10479387 -6.288040e-02
1926 3.10479387 7.487185e+00
1927 11.10479387 5.483444e-01
1928 -15.89520613 -2.284471e+00
1929 -19.03806327 1.262178e+01
1930 -1.89520613 -3.516952e+00
1931 10.60479387 -9.670341e+00
1932 19.10479387 -9.161703e+00
1933 -7.89520613 -2.195930e+00
1934 -10.89520613 3.486362e+00
1935 6.60479387 -8.982388e+00
1936 -9.89520613 4.304070e+00
1937 -11.39520613 2.147820e+00
1938 0.60479387 -6.503853e+00
1939 3.10479387 -1.890126e+00
1940 6.60479387 -1.145521e+01
1941 -0.32377755 -1.091407e+01
1942 -19.89520613 -2.072418e+00
1943 -22.39520613 8.234416e-02
1944 -13.89520613 5.043065e+00
1945 21.10479387 -1.341537e+00
1946 18.60479387 -3.029942e+00
1947 21.47979387 -4.298511e+00
1948 107.10479387 1.348183e+01
1949 33.10479387 8.147820e+00
1950 0.60479387 -1.340275e+00
1951 -10.39520613 -4.842554e-02
1952 22.10479387 1.186976e+01
1953 -2.03806327 1.904855e+00
1954 66.10479387 2.306723e+00
1955 31.10479387 1.556449e+01
1956 15.10479387 2.617386e+01
1957 19.10479387 2.192386e+01
1958 50.10479387 1.432252e+01
1959 13.67622245 6.981154e+00
1960 NA 3.543427e+00
1961 -14.89520613 -5.932375e+00
1962 47.10479387 -7.117811e-01
1963 33.10479387 2.192163e+01
1964 1.10479387 1.558830e+01
1965 -12.77020613 2.440231e+00
1966 4.10479387 2.669107e+00
1967 NA 1.670307e+01
1968 58.10479387 1.416629e+01
1969 49.10479387 5.342155e+00
1970 20.10479387 -4.290430e-01
1971 -23.02020613 9.808535e+00
1972 NA 9.695439e+00
1973 -15.89520613 5.798026e+00
1974 4.10479387 -2.873013e+00
1975 36.10479387 3.012404e+00
1976 22.10479387 1.294130e+01
1977 -0.27020613 2.126602e+01
1978 8.10479387 1.668949e+01
1979 9.10479387 3.511498e+00
1980 -12.89520613 2.958056e+00
1981 21.10479387 2.325720e+01
1982 17.10479387 5.236362e+00
1983 19.81907959 1.285710e+01
1984 19.10479387 1.367386e+01
1985 -14.89520613 1.396032e+01
1986 -14.89520613 3.512404e+00
1987 -15.89520613 6.592114e+00
1988 -6.89520613 8.615747e+00
1989 7.96193673 7.620129e+00
1990 1.10479387 2.128764e+01
1991 27.10479387 2.589261e+01
1992 11.10479387 2.180928e+01
1993 11.10479387 1.359483e+01
1994 42.10479387 2.495511e+01
1995 38.39050816 8.319559e+00
1996 8.10479387 8.189317e+00
1997 NA -2.066482e-01
1998 -31.89520613 1.057385e+00
1999 -24.89520613 1.246779e+00
2000 28.10479387 -5.774799e+00
2001 14.24765102 1.170245e+01
2002 6.10479387 1.254891e+01
2003 16.10479387 4.387957e+00
2004 7.10479387 6.685421e+00
2005 -16.89520613 2.158237e+00
2006 4.10479387 5.684279e+00
2007 19.60479387 1.397387e+01
2008 -15.89520613 9.578376e+00
2009 41.10479387 3.139319e+01
2010 45.10479387 2.755985e+00
2011 -9.89520613 -3.313463e-01
2012 -9.89520613 1.009574e+01
2013 -14.18092041 2.142612e+00
2014 NA -7.015245e-01
2015 25.10479387 -3.681729e-01
2016 32.10479387 9.722498e+00
2017 -1.89520613 -5.540585e+00
2018 -1.89520613 4.667949e+00
2019 -2.27020613 6.476524e+00
2020 -8.89520613 -3.886380e-01
2021 -19.89520613 1.299390e+00
2022 -22.89520613 -7.707031e-01
2023 -14.89520613 4.103208e+00
2024 7.10479387 -6.037566e+00
2025 -5.89520613 -1.685513e+00
2026 -10.89520613 -2.041994e+00
2027 -9.89520613 7.208006e+00
2028 -15.89520613 -4.882505e-01
2029 -26.89520613 1.309254e+00
2030 -4.89520613 -5.462215e-01
2031 -4.89520613 6.846561e-01
2032 -9.89520613 7.494201e+00
2033 -0.89520613 -1.291994e+00
2034 1.10479387 8.561537e-01
2035 -4.89520613 -2.235116e+00
2036 8.10479387 1.162917e+00
2037 -10.77020613 -5.023275e+00
2038 -16.89520613 -5.944772e+00
2039 -14.89520613 9.779331e-01
2040 NA 4.184857e+00
2041 -10.89520613 3.370043e+00
2042 0.10479387 -7.797832e+00
2043 -11.39520613 -6.139217e+00
2044 -9.89520613 2.951584e+00
2045 -5.89520613 1.092882e+01
2046 27.60479387 1.093611e+01
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6788 22.60479387 2.251354e+01
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6802 0.60479387 7.952055e+00
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6851 9.10479387 5.804264e+00
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6864 -21.39520613 -2.489084e+00
6865 -4.39520613 -4.766776e+00
6866 2.10479387 -6.619390e+00
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6870 -15.89520613 -1.116468e+01
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6876 -8.39520613 -9.228732e+00
6877 3.10479387 -7.944442e+00
6878 -8.89520613 6.725201e+00
6879 5.30479387 -8.009718e+00
6880 -6.89520613 -1.249946e+01
6881 -5.39520613 -7.543846e+00
6882 0.60479387 5.441661e+00
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6887 2.60479387 -1.533497e+01
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6890 7.60479387 -1.123760e+01
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6893 -16.89520613 -8.966763e+00
6894 -23.39520613 -1.098443e+01
6895 -6.39520613 -2.466763e+00
6896 -13.39520613 -6.612596e+00
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6899 -16.89520613 -9.616069e+00
6900 -12.89520613 -7.727180e+00
6901 -14.89520613 -6.448194e+00
6902 -20.39520613 -1.262331e+01
6903 -21.39520613 7.258931e+00
6904 -17.89520613 -7.893846e+00
6905 -12.89520613 -1.275496e+01
6906 -17.89520613 -7.768846e+00
6907 -15.39520613 -4.199100e+00
6908 -19.89520613 -7.844480e+00
6909 -16.09520613 -1.024530e+01
6910 -15.39520613 -1.240426e+01
6911 -14.39520613 -1.027926e+01
6912 -13.89520613 -9.102180e+00
6913 -18.39520613 -6.258430e+00
6914 -3.89520613 -1.298760e+01
6915 -0.89520613 -1.473397e+01
6916 5.10479387 -1.551930e+01
6917 -2.89520613 -1.344025e+01
6918 -11.89520613 -1.347718e+01
6919 -3.89520613 -1.030010e+01
6920 -19.89520613 -8.102180e+00
6921 -5.14520613 -1.440426e+01
6922 -12.89520613 -1.280689e+01
6923 -17.89520613 -1.563343e+01
6924 -17.39520613 -1.453968e+01
6925 -11.89520613 -8.268846e+00
6926 -13.89520613 -1.084176e+01
6927 -16.39520613 -5.883430e+00
6928 -12.89520613 -1.137664e+01
6929 -1.89520613 -1.558633e+01
6930 25.60479387 -1.577156e+01
6931 8.60479387 -1.405010e+01
6932 0.60479387 -1.252926e+01
6933 -8.69520613 -1.766468e+01
6934 -25.89520613 -5.081346e+00
6935 -25.39520613 -5.393846e+00
6936 -6.89520613 -1.496676e+01
6937 -6.39520613 -1.617510e+01
6938 -10.39520613 -1.264068e+01
6939 -14.69520613 -1.640109e+01
6940 -10.39520613 -1.690426e+01Note that there are only two columns in the transmuted data frame.
Here’s a table of helper functions specifically associated with mutate():
| Helper Function | Description | Example |
|---|---|---|
if_else() |
A vectorized conditional operation (if-else). | mutate(data, status = if_else(age < 18, "minor", "adult")) |
case_when() |
Generalized multiple conditions for transformations. | mutate(data, category = case_when(score > 90 ~ "A", score > 80 ~ "B", TRUE ~ "C")) |
lead() |
Access the subsequent value in the column. | mutate(data, next_value = lead(column_name)) |
lag() |
Access the preceding value in the column. | mutate(data, previous_value = lag(column_name)) |
row_number() |
Generate row numbers, often used with arrange(). |
mutate(data, rank = row_number()) |
rank(), min_rank(), dense_rank() |
Different types of ranking functions. | mutate(data, rank = rank(score)) |
cumsum(), cumprod(), cummin(), cummax() |
Cumulative functions. | mutate(data, cumulative_total = cumsum(total)) |
coalesce() |
Return the first non-missing value among its arguments. | mutate(data, combined = coalesce(col1, col2)) |
na_if() |
Replace a specified value with NA. | mutate(data, updated_col = na_if(column_name, "replace_me")) |
replace_na() |
Replace NA values with a specified value. | mutate(data, updated_col = replace_na(column_name, "new_value")) |
recode() |
Recode or replace values in a column. | mutate(data, recoded_col = recode(column_name, old="new", ...)) |
across() |
Apply a function across multiple columns (from dplyr 1.0.0). |
mutate(data, across(c(col1, col2), function_name)) |
group_by()
The group_by() function is used to generate summary or aggregate statistics from a data frame.
For example, in this air pollution dataset, you might want to know the average annual level of PM2.5.
So the stratum is the year, which we can derive from the date variable.
In conjunction with the group_by() function we often use the summarize() function. > Or summarise() for some parts of the world.
The general operation here is a combination of splitting a tabel into separate pieces defined by a variable or group of variables (group_by()), and then applying a summary function across those subsets (summarize()), then combining back into another table.
This pattern is called split, apply, and combine. It is a fundamental pattern in data processing.
First, we can create a year variable using as.POSIXlt().
chicago <- chicago %>%
mutate(year = as.POSIXlt(date)$year + 1900)
head(chicago) city tmpd dewpoint date pm25 pm10tmean2 o3tmean2 no2tmean2 pm25detrend
1 chic 31.5 31.500 1987-01-01 NA 34.00000 4.250000 19.98810 NA
2 chic 33.0 29.875 1987-01-02 NA NA 3.304348 23.19099 NA
3 chic 33.0 27.375 1987-01-03 NA 34.16667 3.333333 23.81548 NA
4 chic 29.0 28.625 1987-01-04 NA 47.00000 4.375000 30.43452 NA
5 chic 32.0 28.875 1987-01-05 NA NA 4.750000 30.33333 NA
6 chic 40.0 35.125 1987-01-06 NA 48.00000 5.833333 25.77233 NA
year
1 1987
2 1987
3 1987
4 1987
5 1987
6 1987Now we can create a that computes summary statistics for each year in the data frame with the summarize() function.
years <- chicago %>%
group_by(year) %>%
summarize(pm25 = mean(pm25, na.rm = TRUE),
o3 = max(o3tmean2, na.rm = TRUE),
no2 = median(no2tmean2, na.rm = TRUE), .groups = "drop")
head(years)# A tibble: 6 × 4
year pm25 o3 no2
<dbl> <dbl> <dbl> <dbl>
1 1987 NaN 63.0 23.5
2 1988 NaN 61.7 24.5
3 1989 NaN 59.7 26.1
4 1990 NaN 52.2 22.6
5 1991 NaN 63.1 21.4
6 1992 NaN 50.8 24.8Note in the process, we implicitly created separate data frame that splits the original data frame by year, which is then passed to summarize().
summarize() then returns a data frame with columns for year and the annual averages of pm25, o3, and no2.
In a slightly more complicated example, we might want to know what are the average levels of ozone (o3) and nitrogen dioxide (no2) within quintiles of pm25.
A slicker way to do this would be through a regression model, but we can actually do this quickly with group_by() and summarize().
First, we can create a categorical variable of pm25 divided into quantiles.
qq <- quantile(chicago$pm25, seq(0, 1, 0.2), na.rm = TRUE)
qq 0% 20% 40% 60% 80% 100%
1.700 8.700 12.375 16.700 22.610 61.500 Then can group the data frame by the pm25.quint variable. and compute the mean of o3 and no2 within quantiles of pm25.
chicago %>%
mutate(pm25.quint = cut(pm25, qq)) %>%
group_by(pm25.quint) %>%
summarize(o3 = mean(o3tmean2, na.rm = TRUE),
no2 = mean(no2tmean2, na.rm = TRUE),
.groups = "drop")# A tibble: 6 × 3
pm25.quint o3 no2
<fct> <dbl> <dbl>
1 (1.7,8.7] 21.7 18.0
2 (8.7,12.4] 20.4 22.1
3 (12.4,16.7] 20.7 24.4
4 (16.7,22.6] 19.9 27.3
5 (22.6,61.5] 20.3 29.6
6 <NA> 18.8 25.8From the table, it seems there isn’t a strong relationship between pm25 and o3, but there appears to be a positive correlation between pm25 and no2.
More sophisticated statistical modeling can help to provide precise answers to these questions, but a simple application of dplyr functions can often get you most of the way there.
Here is another example:
chicago %>%
mutate(month = as.POSIXlt(date)$mon + 1) %>%
group_by(month) %>% # SPLIT
summarize(pm25 = mean(pm25, na.rm = TRUE), # APPLY
o3 = max(o3tmean2, na.rm = TRUE),
no2 = median(no2tmean2, na.rm = TRUE),
.groups = "drop")# A tibble: 12 × 4
month pm25 o3 no2
<dbl> <dbl> <dbl> <dbl>
1 1 17.8 28.2 25.4
2 2 20.4 37.4 26.8
3 3 17.4 39.0 26.8
4 4 13.9 47.9 25.0
5 5 14.1 52.8 24.2
6 6 15.9 66.6 25.0
7 7 16.6 59.5 22.4
8 8 16.9 54.0 23.0
9 9 15.9 57.5 24.5
10 10 14.2 47.1 24.2
11 11 15.2 29.5 23.6
12 12 17.5 27.7 24.5 # COMBINE (in the result)Here’s a table of helper functions specifically associated with group_by():
| Helper Function | Description | Example |
|---|---|---|
add_tally() |
Adds a column with the count of each group (equivalent to adding a count with mutate() after a group_by()). |
group_by(data, group_var) %>% add_tally() |
group_size() |
Returns the size of each group. | group_by(data, group_var) %>% summarise(size = group_size()) |
ntile() |
Creates rank percentiles within groups. | group_by(data, group_var) %>% mutate(perc = ntile(score, 4)) |
cur_group_id() |
Gives an integer identifier for the current group. | group_by(data, group_var) %>% filter(cur_group_id() == 1) |
cur_group_rows() |
Provides row indices for the current group. | Used internally, but can be useful for advanced operations. |
group_map(), group_modify(), group_walk() |
Functions to iterate over groups, modify them or walk them with side effects. | group_map(data, ~ head(.x, 2)) shows the first two rows of each group. |
It’s worth noting that group_by() often works in tandem with other verbs, so the real power comes from the combined operations. For instance, after grouping data, one often uses summarise() to calculate summary statistics for each group. The combination of these functions and their associated helpers allow for a wide range of group-wise data manipulation tasks.
Summary
The dplyr package provides a concise set of operations for managing data frames and tibbles.
It allows us to perform a number of complex operations in just a few lines of code.
In particular, we can often conduct the beginnings of an exploratory analysis with the powerful combination of group_by() and summarize().
Once you learn the dplyr grammar there are a few additional benefits — dplyr can work with other data frame “back ends” such as SQL databases. There is an SQL interface for relational databases via the DBI package — dplyr can be integrated with the data.table package for large fast tables
The dplyr package is handy way to both simplify and speed up your data frame management code. It’s rare that you get such a combination at the same time!
Based on Peng 2022