Functions represent some of the most powerful aspects of the R language. And they really represent the transition of the user of R into the kind of programmer of R. And the basic idea is that you can type the command line and kind of explore some data, and run some code. But eventually you'll probably get to the point where you need to do something a little bit more complex. A little bit more than, than can be expressed in a single line or maybe in two lines. And if you have to do this over and over again, then you're usually going to want to encode this kind of functionality in a function. I'm going to talk about functions in three parts here. First I'll talk just about the basics of how to write functions and how they are written, in R. Then I'm going to talk a little bit about lexical scoping and the scoping rules, in, for the R language. And then last, I'm going to end with a little example. So, functions in R are created using the function directive and functions are stored as R objects just like anything else. So you might have a vector of integers a list of different things, a data frame, and then you have a function. So, in particular, R objects, R functions are R objects that are of the class function, okay? So, the basic instruction here is that you assign to some object, here I call it F, the, the function directive, which will take some arguments, and then inside the curly braces there is R, there is R code, which does something that the function does. So one nice thing about R is that functions are con, considered what are called first class objects. So you can treat a function just like you can treat pretty much any other R object. So importantly, this means that you can pass functions as arguments to other functions. This is actually ver, a very useful feature in statistics. And also functions can be nested. So you can define a function inside of another function, and we'll see what the implications of this are we talk about lexical scoping. So the return value of a function is simply the very last R expression in the function value to be evaluated. so, there's no special expression for returning something for a function. Although, there is a function called Return. Which we'll talk about in a second. So functions have what are called named arguments. And the named arguments can potentially have default values. So, a lot of these features are useful for when you're designing functions that, that may be used by other people. For example, you may have a function that had a lot of different arguments so you can tweak a lot of different things. But most of the time, you don't have to change all those different arguments. You may only care about one or two. So it's useful for some of the arguments to have default values. So first of all, there's the formal arguments, which are the arguments that are included in the function definition. So if you go back to the previous slide the formal arguments are the ones that are included inside this function definition here. The formal's function actually will, takes a function as an input and returns a list of all the formal arguments of a function. So not every function call in R makes use of all the formal arguments. So for example, if a, if a function has ten different arguments you may not, you may not have to specify a value for all ten of those arguments. So function arguments can be missing or they may have default values that are used when they are not specified by the users. So R function arguments can be matched positionally or by name. So when, this is very, this is key when you're writing a function and also when you're calling it. So for example, take a look at the function sd, which calculates the standard deviation of, of, of a set of numbers. So sd takes a input x, which is the name of the argument and which is going to be a vector of data. And there's a second argument called na.rm and this controls whether the missing values in the data should be removed or not. And the default value is for na.rm to be equal to false. So by default if you have missing data in your, in the, in the set of numbers for which you want to calculate the standard deviation the missing values will not be included. So, here I'm simulating some data and I'm just simulating a hundred normal random variables, and there's no missing data here. So, if I just calculate sd on the vector it'll give me an estimate of the standard deviation. If I say X equals my data that's the same thing. So here I've named the argument but I haven't but otherwise the data are the same so it'll calculate the standard deviation. In the first example I didn't name the argument. So it defaulted to passing mydata to be the first argument of the function. So in the next example here, I'm going to name both arguments. I'm going to say X equals mydata, and na.rm equals false. That calculates the same thing as before. Now when I name the arguments, I don't have to put them in any special order. So for example, I could reverse the order of the argument here. Say na.rm is equals false first, and then say x equals mydata second, and that will produce exactly the same results because I've named the arguments. Now, what happens if I name one argument and don't name the other? Well what happens is that the named argument is set, and you can figure it as being removed from the argument list, and then any other, any other things that are past will be matched to the function arguments in the order in which they, they come. So for example, SD after you remove the na.rm argument only has one more argument left and so mydata would be assigned to that argument. So all these expressions return the same exact value. So although it's generally, all these expressions are equivalent, I don't say recommend all of them equally. So for example, I don't necessarily recommend reversing the order of the arguments just because you can even though if you name them, it's appropriate. so, just, just because that can lead to some confusion. So positional matching and matching by name can be mixed and this is quite useful often for functions that have very long argument lists. And so for example the lm function here which fits linear models to data has this argument list here. So the first is the formula, the second is the data And then subset, the weights et cetera. And you see that the first five arguments here don't have any default value. So, the user has to specify them. So the but then the method, the model, the X argument, they all have default values so if you don't specify them they will use those values by default. And so the following two function calls are equivalent. I could have specified the data first and then the formula and then the model. And then, and then, and then the subset arguments or I could specify the formula first, the data second, the subset and then say model is equal to false. Now the reason why the first one is okay is because I, so I matched the data argument by name. You can imagine that that's kind of taken out of the argument list now, then Y till the X doesn't, isn't specified by name. So it's given to the first argument that hasn't already been matched. And I, in which case that's the formula. Model equal to false, so that's been matched by name so I can kind of get rid of that from the argument list. And then 1 through 100 has to be assigned to the argument that has not yet already been matched. So in this case formula was already matched, data was already matched. And so the next one is subset. So 1 to 100 get's assigned to the subset argument. So this is somewhat a confusing way to call lm, and I don't recommend that you do it this way. But, I, I wrote it this way just to demonstrate how positional matching, and matching by name can work together. A common usage for lm though is the second version here. Which say lm Y til the X. So there is a formula there. And then the next one is mydata, which the data set which you're going to grab the data from. The subset argument and then, so the first three arguments, you know, are commonly specified, every time you call lm. But then, the rest you may or may not specify and so you may, if you just want to specify one of the following arguments. It's easier just to call it out by name. so, most of the time, the named arguments are useful in the command line. When you have a long argument list and you want to use the defaults for everything except for one of the arguments, which may be in the middle or near the end of the list, and you can't usually, you know, you can't remember exactly which argument it is, whether it's the fourth, or the sixth, or the tenth argument on the argument list. And so you just call it by name, and that way you don't have to remember the order of the arguments on the argument list. Another example where this comes in handy is for plotting, because mo, many of the plot functions have very long argument lists. All of which have default values and you may only want to tweak one specific argument. And so it's useful not to have to remember, you know, what the order of that argument is on the arg, on the argument list. So function arguments can, can also be partially matched which is used, mostly useful primarily for interactive work, not so much for programming. But when you call a function, if the argument has a very long name you can match it partially so you can type part of the argument name and as long as there's a unique match there then it will, the R system will match the argument and assign the value to, to, to the correct one. So the, the, the order of the operations that R uses, first it'll check for an exact match. So if you name an argument it'll check, check to see if there's an argument that, that exactly matches that name. If there's no exact match it'll look for a partial match. And then if that doesn't work, it'll look for a positional match.