Have you ever thought about why the definition of a function in R is different from many other programming languages? The part that causes the biggest difficulties (especially for beginners of R) is that you state the name of the function at the beginning and use the assignment operator – as if functions were like any other data type, like vectors, matrices or data frames…
Congratulations! You just encountered one of the big ideas of functional programming: functions are indeed like any other data type, they are not special – or in programming lingo, functions are first-class members. Now, you might ask: So what? Well, there are many ramifications, for example that you could use functions on other functions by using one function as an argument for another function. Sounds complicated?
In mathematics most of you will be familiar with taking the derivative of a function. When you think about it you could say that you put one function into the derivative function (or operator) and get out another function!
In R there are many applications as well, let us go through a simple example step by step.
Let’s say I want to apply the mean function on the first four columns of the iris dataset. I could do the following:
Quite tedious and not very elegant. Of course, we can use a for loop for that:
This works fine but there is an even more intuitive approach. Just look at the original task: “apply the mean function on the first four columns of the iris dataset” – so let us do just that:
Wow, this is very concise and works perfectly (the 2 just stands for “go through the data column wise”, 1 would be for “row wise”). apply is called a “higher-order function” and we could use it with all kinds of other functions:
You can also use user-defined functions:
We can even use new functions that are defined “on the fly” (or in functional programming lingo “anonymous functions”):
Let us now switch to another inbuilt data set, the mtcars dataset with 11 different variables of 32 cars (if you want to find out more, please consult the documentation):
To see the power of higher-order functions let us create a (numeric) matrix with minimum, first quartile, median, mean, third quartile and maximum for all 11 columns of the mtcars dataset with just one command!
Wow, that was easy and the result is quite impressive, is it not!
Or if you want to perform a linear regression for all ten variables separately against mpg and want to get a table with all coefficients – there you go:
Here we used another higher-order function, sapply, together with an anonymous function. sapply goes through all the columns of a data frame (i.e. elements of a list) and tries to simplify the result (here your get back a nice matrix).
Often, you might not even have realised when you were using higher-order functions! I can tell you that it is quite a hassle in many programming languages to program a simple function plotter, i.e. a function which plots another function. In R it has already been done for you: you just use the higher-order function curve and give it the function you want to plot as an argument:
I want to give you one last example of another very helpful higher-order function (which not too many people know or use): by. It comes in very handy when you want to apply a function on different attributes split by a factor. So let’s say you want to get a summary of all the attributes of iris split by (!) species – here it comes:
This was just a very shy look at this huge topic. There are very powerful higher-order functions in R, like lapppy, aggregate, replicate (very handy for numerical simulations) and many more. A good overview can be found in the answers of this question: stackoverflow (my answer there is on the rather illusive switch function: switch).
For some reason people tend to confuse higher-order functions with recursive functions but that is the topic of another post, so stay tuned…
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