One part of reducing duplication is writing functions. Functions allow you to identify repeated patterns of code and extract them out in to indepdent pieces that you can reuse and easily update as code changes. Iteration helps you when you need to do the same thing to multiple inputs: repeating the same operation on different columns, or on different datasets. (Generally, you shouldn't need to use explicit iteration to deal with different subsets of your data: in most cases the implicit iteration in dplyr will take care of that problem for you.)
In this chapter you'll learn about two important iteration tools: for loops and functional programming. For loops are a great place to start because they make iteration very explicit, so that it's obvious what's happening. However, that explicitness is also the downside of for loops: they are quite verbose, and include quite a bit of book-keeping code. The one of the goals of functional programming is to extract out common patterns of for loops into their own functions. Once you master the vocabulary this allows you to solve many common iteration problems with less code, more ease, and less chance of errors.
Sometimes you might know now how long the output will be. There is one common pattern that has a relatively simple work around. For example, imagine you want to simulate some random numbers:
In general this loop isn't going to be very efficient because in each iteration, R has to copy all the data from the previous iterations. In technical terms you get "quadratic" behaviour which means that a loop with three times as many elements would take nine times ($3^2$) as long to run.
```{r}
out <- vector("list", length(means))
for (i in seq_along(means)) {
n <- sample(100, 1)
out[[i]] <- rnorm(n, means[[i]])
}
str(out)
```
Then you can use a function list `unlist()`, or `purrr::flatten_dbl()` to collapse this to a simple vector. This pattern occurs in other places too:
1. You might be generating a long string. Instead of `paste()`ing together each
iteration, save the results in a character vector and then run
`paste(results, collapse = "")` to combine the individual results into
a single string.
1. You might generating a big data frame. Instead of `rbind()` the results
together on each run, save the results in list and then use
`dplyr::bind_rows(results)` to combine the results into a single
For loops are not as important in R as they are in other languages as rather than writing your own for loops, you'll typically use prewritten functions that wrap up common for-loop patterns. These functions are important because they wrap up the book-keeping code related to the for loop, focussing purely on what's happening.
Imagine you have a data frame and you want to compute the mean of each column. You might write code like this:
```{r}
df <- data.frame(
a = rnorm(10),
b = rnorm(10),
c = rnorm(10),
d = rnorm(10)
)
results <- numeric(length(df))
for (i in seq_along(df)) {
results[i] <- mean(df[[i]])
}
results
```
(Here we're taking advantage of the fact that a data frame is a list of the individual columns, so `length()` and `seq_along()` are useful.)
You realise that you're going to want to compute the means of every column pretty frequently, so you extract it out into a function:
```{r}
col_mean <- function(df) {
results <- numeric(length(df))
for (i in seq_along(df)) {
results[i] <- mean(df[[i]])
}
results
}
```
But then you think it'd also be helpful to be able to compute the median or the standard deviation:
```{r}
col_median <- function(df) {
results <- numeric(length(df))
for (i in seq_along(df)) {
results[i] <- median(df[[i]])
}
results
}
col_sd <- function(df) {
results <- numeric(length(df))
for (i in seq_along(df)) {
results[i] <- sd(df[[i]])
}
results
}
```
I've now copied-and-pasted this function three times, so it's time to think about how to generalise it. Most of the code is for-loop boilerplate and it's hard to see the one piece (`mean()`, `median()`, `sd()`) that differs.
What would you do if you saw a set of functions like this:
```{r}
f1 <- function(x) abs(x - mean(x)) ^ 1
f2 <- function(x) abs(x - mean(x)) ^ 2
f3 <- function(x) abs(x - mean(x)) ^ 3
```
Hopefully, you'd notice that there's a lot of duplication, and extract it out into an additional argument:
```{r}
f <- function(x, i) abs(x - mean(x)) ^ i
```
You've reduce the chance of bugs (because you now have 1/3 less code), and made it easy to generalise to new situations. We can do exactly the same thing with `col_mean()`, `col_median()` and `col_sd()`, by adding an argument that contains the function to apply to each column:
The idea of using a function as an argument to another function is extremely powerful. It might take you a while to wrap your head around it, but it's worth the investment. In the rest of the chapter, you'll learn about and use the __purrr__ package which provides a set of functions that eliminate the need for for-loops for many common scenarios. The apply family of functions in base R (`apply()`, `lapply()`, `tapply()`, etc) solve a similar problem, but purrr is more consistent and thus is easier to learn.
The goal of using purrr functions instead of for loops is to allow you break common list manipulation challenges into independent pieces:
1. How can you solve the problem for a single element of the list? Once
you've solved that problem, purrr takes care of generalising your
solution to every element in the list.
1. If you're solving a complex problem, how can you break it down into
bite sized pieces that allow you to advance one small step towards a
solution? With purrr, you get lots of small pieces that you can
compose together with the pipe.
This structure makes it easier to solve new problems. It also makes it easier to understand your solutions to old problems when you re-read your old code.
In later chapters you'll learn how to apply these ideas when modelling. You can often use multiple simple models to help understand a complex dataset, or you might have multiple models because you're bootstrapping or cross-validating. The techniques you'll learn in this chapter will be invaluable.
The pattern of looping over a list and doing something to each element is so common that the purrr package provides a family of functions to do it for you. Each function always returns the same type of output so there are six variations based on what sort of result you want:
* `walk()` returns nothing. Walk is a little different to the others because
it's called exclusively for its side effects, so it's described in more detail
later in [walk](#walk).
Each function takes a list as input, applies a function to each piece, and then returns a new vector that's the same length as the input. The type of the vector is determined by the specific map function. Usually you want to use the most specific available, using `map()` only as a fallback when there is no specialised equivalent available.
We can use these functions to perform the same computations as the previous for loops:
Compared to using a for loop, focus is on the operation being performed (i.e. `mean()`, `median()`, `sd()`), not the book-keeping required to loop over every element and store the results.
* The second argument, `.f`, the function to apply, can be a formula, a
character vector, or an integer vector. You'll learn about those handy
shortcuts in the next section.
* Any arguments after `.f` will be passed on to it each time it's called:
```{r}
map_dbl(df, mean, trim = 0.5)
```
* The map functions also preserve names:
```{r}
z <- list(x = 1:3, y = 4:5)
map_int(z, length)
```
### Shortcuts
There are a few shortcuts that you can use with `.f` in order to save a little typing. Imagine you want to fit a linear model to each group in a dataset. The following toy example splits the up the `mtcars` dataset in to three pieces (one for each value of cylinder) and fits the same linear model to each piece:
```{r}
models <- mtcars %>%
split(.$cyl) %>%
map(function(df) lm(mpg ~ wt, data = df))
```
The syntax for creating an anonymous function in R is quite verbose so purrr provides a convenient shortcut: a one-sided formula.
```{r}
models <- mtcars %>%
split(.$cyl) %>%
map(~lm(mpg ~ wt, data = .))
```
Here I've used `.` as a pronoun: it refers to the current list element (in the same way that `i` referred to the current index in the for loop). You can also use `.x` and `.y` to refer to up to two arguments. If you want to create a function with more than two arguments, do it the regular way!
When you're looking at many models, you might want to extract a summary statistic like the $R^2$. To do that we need to first run `summary()` and then extract the component called `r.squared`. We could do that using the shorthand for anonymous functions:
```{r}
models %>%
map(summary) %>%
map_dbl(~.$r.squared)
```
But extracting named components is a common operation, so purrr provides an even shorter shortcut: you can use a string.
```{r}
models %>%
map(summary) %>%
map_dbl("r.squared")
```
You can also use a numeric vector to select elements by position:
1. What happens when you use the map functions on vectors that aren't lists?
What does `map(1:5, runif)` do? Why?
1. What does `map(-2:2, rnorm, n = 5)` do. Why?
1. Rewrite `map(x, function(df) lm(mpg ~ wt, data = df))` to eliminate the
anonymous function.
## Dealing with failure
When you do many operations on a list, sometimes one will fail. When this happens, you'll get an error message, and no output. This is annoying: why does one failure prevent you from accessing all the other successes? How do you ensure that one bad apple doesn't ruin the whole barrel?
In this section you'll learn how to deal this situation with a new function: `safely()`. `safely()` is an adverb: it takes a function (a verb) and returns a modified version. In this case, the modified function will never throw an error. Instead, it always returns a list with two elements:
1. `result` is the original result. If there was an error, this will be `NULL`.
1. `error` is an error object. If the operation was successful this will be
`NULL`.
(You might be familiar with the `try()` function in base R. It's similar, but because it sometimes returns the original result and it sometimes returns an error object it's more difficult to work with.)
Let's illustrate this with a simple example: `log()`:
```{r}
safe_log <- safely(log)
str(safe_log(10))
str(safe_log("a"))
```
When the function succeeds the `result` element contains the result and the `error` element is `NULL`. When the function fails, the `result` element is `NULL` and the `error` element contains an error object.
`safely()` is designed to work with map:
```{r}
x <- list(1, 10, "a")
y <- x %>% map(safely(log))
str(y)
```
This would be easier to work with if we had two lists: one of all the errors and one of all the results. That's easy to get with `transpose()`.
```{r}
y <- y %>% transpose()
str(y)
```
It's up to you how to deal with the errors, but typically you'll either look at the values of `x` where `y` is an error or work with the values of y that are ok:
```{r}
is_ok <- y$error %>% map_lgl(is_null)
x[!is_ok]
y$result[is_ok] %>% flatten_dbl()
```
Purrr provides two other useful adverbs:
* Like `safely()`, `possibly()` always succeeds. It's simpler than `safely()`,
because you give it a default value to return when there is an error.
```{r}
x <- list(1, 10, "a")
x %>% map_dbl(possibly(log, NA_real_))
```
* `quietly()` performs a similar role to `safely()`, but instead of capturing
errors, it captures printed output, messages, and warnings:
```{r}
x <- list(1, -1)
x %>% map(quietly(log)) %>% str()
```
### Exercises
1. Challenge: read all the csv files in this directory. Which ones failed
So far we've mapped along a single list. But often you have multiple related lists that you need iterate along in parallel. That's the job of the `map2()` and `pmap()` functions. For example, imagine you want to simulate some random normals with different means. You know how to do that with `map()`:
```{r}
mu <- list(5, 10, -3)
mu %>% map(rnorm, n = 10)
```
What if you also want to vary the standard deviation? You need to iterate along a vector of means and a vector of standard deviations in parallel. That's a job for `map2()` which works with two parallel sets of inputs:
The arguments that vary for each call come before the function name, and arguments that are the same for every function call come afterwards.
Like `map()`, `map2()` is just a wrapper around a for loop:
```{r}
map2 <- function(x, y, f, ...) {
out <- vector("list", length(x))
for (i in seq_along(x)) {
out[[i]] <- f(x[[i]], y[[i]], ...)
}
out
}
```
You could also imagine `map3()`, `map4()`, `map5()`, `map6()` etc, but that would get tedious quickly. Instead, purrr provides `pmap()` which takes a list of arguments. You might use that if you wanted to vary the mean, standard deviation, and number of samples:
As soon as your code gets complicated, I think a data frame is a good approach because it ensures that each column has a name and is the same length as all the other columns. We'll come back to this idea when we explore the intersection of dplyr, purrr, and model fitting.
### Invoking different functions
There's one more step up in complexity - as well as varying the arguments to the function you might also vary the function itself:
The first argument is a list of functions or character vector of function names. The second argument is a list of lists giving the arguments that vary for each function. The subsequent arguments are passed on to every function.
You can use `dplyr::frame_data()` to make creating these matching pairs a little easier:
```{r, eval = FALSE}
# Needs dev version of dplyr
sim <- dplyr::frame_data(
~f, ~params,
"runif", list(min = -1, max = -1),
"rnorm", list(sd = 5),
"rpois", list(lambda = 10)
)
sim %>% dplyr::mutate(
samples = invoke_map(f, params, n = 10)
)
```
## Walk {#walk}
Walk is an alternative to map that you use when you want to call a function for its side effects, rather than for its return value. You typically do this because you want to render output to the screen or save files to disk - the important thing is the action, not the return value. Here's a very simple example:
```{r}
x <- list(1, "a", 3)
x %>%
walk(print)
```
`walk()` is generally not that useful compared to `walk2()` or `pwalk()`. For example, if you had a list of plots and a vector of file names, you could use `pwalk()` to save each file to the corresponding location on disk:
Imagine we want to summarise each numeric column of a data frame. We could do it in two steps:
1. Find all numeric columns.
1. Summarise each column.
In code, that would look like:
```{r}
col_sum <- function(df, f) {
is_num <- df %>% map_lgl(is_numeric)
df[is_num] %>% map_dbl(f)
}
```
`is_numeric()` is a __predicate__: a function that returns either `TRUE` or `FALSE`. There are a number of of purrr functions designed to work specifically with predicates:
* `keep()` and `discard()` keeps/discards list elements where the predicate is
true.
* `head_while()` and `tail_while()` keep the first/last elements of a list until
you get the first element where the predicate is true.
* `some()` and `every()` determine if the predicate is true for any or all of
the elements.
* `detect()` and `detect_index()`
We could use `keep()` to simplify the summary function to:
```{r}
col_sum <- function(df, f) {
df %>%
keep(is.numeric) %>%
map_dbl(f)
}
```
I like this formulation because you can easily read the sequence of steps.
### Exercises
1. A possible base R equivalent of `col_sum()` is:
```{r}
col_sum3 <- function(df, f) {
is_num <- sapply(df, is.numeric)
df_num <- df[, is_num]
sapply(df_num, f)
}
```
But it has a number of bugs as illustrated with the following inputs:
```{r, eval = FALSE}
df <- data.frame(z = c("a", "b", "c"), x = 1:3, y = 3:1)
# OK
col_sum3(df, mean)
# Has problems: don't always return numeric vector
