The R for Data Science (R4DS) book by Hadley Wickham is a definite must-read for every R programmer. Amongst others, the power of functional programming is explained in it very well in the chapter on Iteration. I wrote about functional programming before, but I recently re-read the R4DS book section after coming across some new valuable resources on particularly R’s purrr functions.

The purpose of this blog post is twofold. First, I wanted to share these new resources I came across, along with the other resources I already have collected over time on functional programming. Second, I wanted to demonstrate via code why functional programming is so powerful, and how it can speed up, clean, and improve your own workflow.


1. Resources

So first things first, “what are these new functional programming resources?”, you must be wondering. Well, here they are:

The good old go-to resource for anyone trying to learn purrr is Jenny Brian’s tutorial.

Nevertheless, Emorie Beck made a another great tutorial, specifically dealing with running and visualizing multiple linear models.

Thomas Mock was as inspired by the R4DS book as I was, and will run you through the details behind some of the examples in this tutorial

Hadley Wickham himself gave a talk at a 2016 EdinbR meetup, explaing why and how to (1) use tidyr to make nested data frame, (2) use purrr for functional programming instead of for loops, and (3) visualise models by converting them to tidy data with broom:

Via YouTube.

Colin Fay dedicated several blogs to purrr. Some are very helpful as introduction — particularly this one — others demonstrate more expert applications of the power of purrr — such as this sequence of six blogs on web mining

This GitHub repository by Dan Ovando does a fantastic job of explaining functional programming and demonstrating the functionality of purrr.

Cormac Nolan made a beautiful RPub Markdown where he displays how functional programming in combination with purrr‘s functions can result in very concise, fast, and supercharged code. 

Of course, we shouldn’t forget the purrr cheat sheet by RStudio. 

A more general resource, DataCamp hosts this fantastic course on writing functions by Hadley and Charlotte Wickham. And while you’re at it, do also read the R4DS chapter on writing functions!

Last, but not least, part of Duke University 2017’s statistical programming course can be found here, related to functional programming with and without purrr


2. Functional programming example

I wanted to run you through the basics behind functional programming, the apply family and their purrring successors. I try to do so by providing you some code which you can run in R yourself alongside this read. The content is very much inspired on the R4DS book chapter on iteration.

Let’s start with some data

# let's grab a subset of the mtcars dataset
mtc <- mtcars[ , 1:3] # store the first three columns in a new object

Say we would like to know the average (mean) value of the data in each of the columns of this new dataset. A starting programmer would usually write something like the below:

#### basic approach:

mean(mtc$mpg)
mean(mtc$cyl)
mean(mtc$disp)

However, this approach breaks the rule of three!
Bascially, we want to avoid copying and pasting anything more than twice.

A basic solution would be to use a for-loop to iterate through each column’s data one by one, and calculate and store the mean for each.
Here, we first want to pre-allocate an output vector, in order to prevent that we grow (and copy into memory) a vector in each of the iterations of our for-loop. Details regarding why you do not want to grow a vector can be found here. A similar memory-issue you can create with for-loops is described here.

In the end, our for-loop approach to calculating column means could look something like this:

#### for loop approach:

output <- vector("double", ncol(mtc)) # pre-allocate an empty vector

# replace each value in the vector by the column mean using a for loop
for(i in seq_along(mtc)){
output[i] <- mean(mtc[[i]])
}

# print the output
output
[1]  20.09062   6.18750 230.72188

This output is obviously correct, and the for-loop does the job, however, we are left with some unnecessary data created in our global environment, which not only takes up memory, but also creates clutter.

ls() # inspect global environment
[1] "i" "mtc" "output"

Let’s remove the clutter and move on.

rm(i, output) # remove clutter

Now, R is a functional programming language so this means that we can write our own function with for-loops in it! This way we prevent the unnecessary allocation of memory to overhead variables like i and output. For instance, take the example below, where we create a custom function to calculate the column means. Note that we still want to pre-allocate a vector to store our results.

#### functional programming approach:

col_mean <- function(df) {
output <- vector("double", length(df))
for (i in seq_along(df)) {
output[i] <- mean(df[[i]])
}
output
}

Now, we can call this standardized piece of code by calling the function in different contexts:

col_mean(mtc)
col_mean(mtcars)
col_mean(iris[1:4])
[1]  20.09062   6.18750 230.72188

[1] 20.090625 6.187500 230.721875 146.687500 3.596563 3.217250 17.848750 0.437500 0.406250 3.687500 2.812500

[1] 5.843333 3.057333 3.758000 1.199333

This way we prevent that we have to write the same code multiple times, thus preventing errors and typos, and we are sure of a standardized output.

Moreover, this functional programming approach does not create unnecessary clutter in our global environment. The variables created in the for loop (i and output) only exist in the local environment of the function, and are removed once the function call finishes. Check for yourself, only our dataset and our user-defined function col_mean remain:

ls()
[1] "col_mean" "mtc"   

For the specific purpose we are demonstrating here, a more flexible approach than our custom function already exists in base R: in the form of the apply family. It’s a set of functions with internal loops in order to “apply” a function over the elements of an object. Let’s look at some example applications for our specific problem where we want to calculate the mean values for all columns of our dataset. 

#### apply approach:

# apply loops a function over the margin of a dataset
apply(mtc, MARGIN = 1, mean) # either by its rows (MARGIN = 1)
apply(mtc, MARGIN = 2, mean) # or over the columns (MARGIN = 2)

# in both cases apply returns the results in a vector
# sapply loops a function over the columns, returning the results in a vector
sapply(mtc, mean)
  mpg       cyl      disp 
20.09062 6.18750 230.72188
# lapply loops a function over the columns, returning the results in a list
lapply(mtc, mean)
$mpg
[1] 20.09062
$cyl
[1] 6.1875
$disp
[1] 230.7219

Sidenote: sapply and lapply both loop their input function over a dataframe’s columns by default as R dataframes are actually lists of equal-length vectors (see Advanced R [Wickham, 2014]).

# tapply loops a function over a vector 
# grouping it by a second INDEX vector
# and returning the results in a vector
tapply(mtc$mpg, INDEX = mtc$cyl, mean)
   4        6        8 
26.66364 19.74286 15.10000

These apply functions are a cleaner approach than the prior for-loops, as the output is more predictable (standard a vector or a list) and no unnecessary variables are allocated in our global environment.

Performing the same action to each element of an object and saving the results is so common in programming that our friends at RStudio decided to create the purrr package. It provides another family of functions to do these actions for you in a cleaner and more versatile approach building on
functional programming.

install.packages("purrr")
library("purrr")

Like the apply family, there are multiple functions that each return a specific output:

# map returns a list.
map(mtc, mean)
$mpg
[1] 20.09062
$cyl
[1] 6.1875
$disp
[1] 230.7219
# map_lgl returns a logical vector
# as numeric means aren't often logical, I had to call a different function
map_lgl(mtc, is.logical) # mtc's columns are numerical, hence FALSE
mpg   cyl  disp 
FALSE FALSE FALSE
# map_int returns an integer vector
# as numeric means aren't often integers, I had to call a different function
map_int(mtc, is.integer) # returned FALSE, which is converted to integer (0)
mpg  cyl disp 
0 0 0
#map_dbl returns a double vector.
map_dbl(mtc, mean)
  mpg       cyl      disp 
20.09062 6.18750 230.72188
# map_chr returns a character vector.
map_chr(mtc, mean)
     mpg          cyl         disp 
"20.090625" "6.187500" "230.721875"

All purrr functions are implemented in C. This makes them a little faster at the expense of readability. Moreover, the purrr functions can take in additional arguments. For instance, in the below example, the na.rm argument is passed to the mean function 

map_dbl(rbind(mtc, c(NA, NA, NA)), mean) # returns NA due to the row of missing values
map_dbl(rbind(mtc, c(NA, NA, NA)), mean, na.rm = TRUE) # handles those NAs
mpg  cyl disp 
NA NA NA

mpg cyl disp
20.09062 6.18750 230.72188

Once you get familiar with purrr, it becomes a very powerful tool. For instance, in the below example, we split our little dataset in groups for cyl and then run a linear model within each group, returning these models as a list (standard output of map). All with only three lines of code!

mtc %>% 
split(.$cyl) %>%
map(~ lm(mpg ~ disp, data = .))
$4
Call:
lm(formula = mpg ~ disp, data = .)
Coefficients:
(Intercept) disp
40.8720 -0.1351
$6
Call:
lm(formula = mpg ~ disp, data = .)
Coefficients:
(Intercept) disp
19.081987 0.003605
$8
Call:
lm(formula = mpg ~ disp, data = .)
Coefficients:
(Intercept) disp
22.03280 -0.01963

We can expand this as we go, for instance, by inputting this list of linear models into another map function where we run a model summary, and then extract the model coefficient using another subsequent map:

mtc %>% 
split(.$cyl) %>%
map(~ lm(mpg ~ disp, data = .)) %>%
map(summary) %>% # returns a list of linear model summaries
map("coefficients")
$4
Estimate Std. Error t value Pr(>|t|)
(Intercept) 40.8719553 3.58960540 11.386197 1.202715e-06
disp -0.1351418 0.03317161 -4.074021 2.782827e-03
$6
Estimate Std. Error t value Pr(>|t|)
(Intercept) 19.081987419 2.91399289 6.5483988 0.001243968
disp 0.003605119 0.01555711 0.2317344 0.825929685
$8
Estimate Std. Error t value Pr(>|t|)
(Intercept) 22.03279891 3.345241115 6.586311 2.588765e-05
disp -0.01963409 0.009315926 -2.107584 5.677488e-02

The possibilities are endless,
our code is fast and readable,
our function calls provide predictable return values,
and our environment stays clean!

If you want to learn more, please do have a look at the earlier resources and the R4DS book chapters on functions and iterations in particular!


PS. sorry for the terrible layout but WordPress really has been acting up lately… I really should move to some other blog hosting method. Any tips? Potentially Jekyll?