When you create faster versions, you can compare the results to make sure your fast versions are still correct. Once you get through most of the FE map, you will get 1 Hover Tank. Find local businesses, view maps and get driving directions in Google Maps. That means that the following two function calls should return the same value: This implies that add(NA, NA, na.rm = TRUE) must be 0, and hence identity = 0 is the correct default. Section 2.2.1. The following sections build on lapply() and discuss: sapply() and vapply(), variants of lapply() that produce vectors, matrices, and arrays as output, instead of lists. (“Map” also has the nice property of being short, which is useful for such a fundamental building block.). View the Quick Start Guide View the Full User Manual. There are a couple of ways to deal with this. First we generate some sample data: To solve this challenge we need to use intersect() repeatedly: reduce() automates this solution for us, so we can write: We could apply the same idea if we wanted to list all the elements that appear in at least one entry. vapply() returns a vector but it requires us to loop over a set of indices. important variants of This allows us to write a version of add() that can deal with missing values if needed: Why did we pick an identity of 0? Functional programming teaches you about the powerful Reduce() and Filter() functions which are useful for working with lists. Find() returns the first element which matches the predicate (or the last element if right = TRUE). similar issues to sapply(). Calling Reduce(f, 1:3) is equivalent to f(f(1, 2), 3). In base R functions, like lapply(), you can provide the name of the function as a string. Use both for loops and lapply() to fit linear models to the mtcars using the formulas stored in this list: Fit the model mpg ~ disp to each of the bootstrap replicates of mtcars in the list below by using a for loop and lapply(). Static mapping is straightforward with plot (), as we saw in Section 2.2.3. If you’re struggling to solve a problem using one form, you might find it easier with another. knitr, and it returns the result that it does? function is the identity operator, the output is not always the same as In this case we can remove the loop by recognising a special feature of the problem. Why isn’t is.na() a predicate function? There are a few caveats to using apply(). reduce() takes a vector of length n and produces a vector of length 1 by calling a function with a pair of values at a time: reduce(1:4, f) is equivalent to f(f(f(1, 2), 3), 4). Functionals play other roles as well as replacements for for-loops. This is the reason why the arguments to map() are a little odd: instead of being x and f, they are .x and .f. This means that apply() is not safe to use inside a function unless you carefully check the inputs. Implement mcsapply(), a multicore version of sapply(). How could you improve them? sapply() and vapply() are very similar to lapply() except they simplify their output to produce an atomic vector. Never use apply() with a data frame. In this section, we’ll give a brief overview of the available options, hint at how they can help you, and point you in the right direction to learn more. You can make it a little clearer by abandoning the ~ helper: Sometimes, if you want to be (too) clever, you can take advantage of R’s Data structure functionals discusses functionals that work with more complex data structures like matrices and arrays. How do you get the result in this picture? In MLE, we have two sets of parameters: the data, which is fixed for a given problem, and the parameters, which vary as we try to find the maximum. Advanced Map Trainer. My first functional: lapply() introduces your first functional: lapply(). For loops have a bad rap in R because many people believe they are slow51, but the real downside of for loops is that they’re very flexible: a loop conveys that you’re iterating, but not what should be done with the results. We’ll cover three categories of data structure functionals: apply(), sweep(), and outer() work with matrices. X and FUN). When given a data frame, sapply() and vapply() return the same results. Implement arg_max(). The base equivalent to map() is lapply(). Returning to our example from Section 9.2.5, where we wanted to vary the trim argument to x, we could instead use pmap(): I think it’s good practice to name the components of the list to make it very clear how the function will be called. to being a predicate version of is.na()? This is the companion website for “Advanced R”, a book in Chapman & Hall’s R Series.The book is designed primarily for R users who want to improve … If you need to modify part of an existing data frame, it’s often better to use a for loop. predicate function f, span(x, f) returns the location of the longest There are two base equivalents to the pmap() family: Map() and mapply(). Many are written in C, and use special tricks to enhance performance. If an argument after f is a vector, it will be passed along as is: (You’ll learn about map variants that are vectorised over multiple arguments in Sections 9.4.2 and 9.4.5.). This makes undesired matches extremely Challenge: read about the fixed point algorithm. Without additional arguments, reduce() just returns the input when x is length 1: This means that reduce() has no way to check that the input is valid: What if it’s length 0? Avoid copies discusses this problem in more depth. keep(.x, .p) keeps all matching elements; What are the sep and collapse arguments to paste() equivalent to? Functionals implemented in base R are well tested (i.e., bug-free) and efficient, because they’re used by so many people. What does replicate() do? Now you can see how simple and powerful the underlying idea is: map-reduce is a map combined with a reduce. This chapter will focus on functionals provided by the purrr package.52 These functions have a consistent interface that makes it easier to understand the key ideas than their base equivalents, which have grown organically over many years. In this section we’ll use some of R’s built-in mathematical functionals. might find rle() helpful.). lapply() is the building block for many other functionals, so it’s important to understand how it works. This lets us write: Note that the order of arguments is a little different: function is the first argument for Map() and the second for lapply(). This means that they are not very consistent: With tapply() and sapply(), the simplify argument is called simplify. This means both .x and .y are varied in each call to .f: The arguments to map2() are slightly different to the arguments to map() as two vectors come before the function, rather than one. Note how the closure allows us to precompute values that are constant with respect to the data. © Hadley Wickham. The easiest way to fix this problem is to use the init argument of Reduce(). Instead, it helps you clearly communicate and build tools that solve a wide range of problems. Each functional is tailored for a specific task, so when you recognise the functional you immediately know why it’s being used. First, we create a function factory that, given a dataset, returns a function that computes the negative log likelihood (NLL) for parameter lambda. We can’t eliminate the for loop because none of the functionals we’ve seen allow the output at position i to depend on both the input and output at position i - 1. the plyr package, which generalises tapply() to make it easy to work with data frames, lists, or arrays as inputs, and data frames, lists, or arrays as outputs. Section 9.4 teaches you about 18 (!!) 18-12-2013 . of 1 variable: #> $ y: Factor w/ 3 levels "a","b","c": 1 2 3, #> Factor w/ 3 levels "a","b","c": 1 2 3, #> [1] 0.7299003 0.6912574 0.3974208 0.2609422 0.6152912 0.5044094 NA, Loops that shouldn’t be converted to functions, “The R apply function - a tutorial with examples”, “The Split-Apply-Combine Strategy for Data Analysis”. Very occasionally you need to pass two arguments to the function that you’re reducing. A common use of functionals is as an alternative to for loops. It is better suited for use inside other functions. There are two main reasons: Since all variants were implemented by combining a simple binary operator (add()) and a well-tested functional (Reduce(), Map(), apply()), we know that our variants will behave consistently. For example, in this example you can rewrite (The argument name comes from thinking about Just replace the loop with lapply() by using <<-: The for loop is gone, but the code is longer and much harder to understand. Use sapply() and an anonymous function to extract the p-value from every trial. The following two examples show what Reduce does with an infix and prefix function: The essence of Reduce() can be described by a simple for loop: The real Reduce() is more complicated because it includes arguments to control whether the values are reduced from the left or from the right (right), an optional initial value (init), and an option to output intermediate results (accumulate). The book is designed primarily for R users who want to improve their programming skills and understanding of the language. It’s a little different in that it takes multiple vector inputs and creates a matrix or array output where the input function is run over every combination of the inputs: Good places to learn more about apply() and friends are: “Using apply, sapply, lapply in R” by Peter Werner. Both have significant drawbacks: Map() vectorises over all arguments so you cannot supply arguments that For example, how would you find a weighted mean when you have a list of observations and a list of weights? Fortunately, their orthogonal design makes them easy to Making Maps with R Intro. We allocate a list the same length as the input, and then fill in the list with a for loop. #> 'data.frame': 3 obs. It is often used with apply() to standardise arrays. Just as it’s better to use while than repeat, and it’s better to use for than while (Section 5.3.2), it’s better to use a functional than for. In Section 9.6.2 you’ll learn about a very useful variant of modify(), called modify_if(). Instead, it’s much better to create the space you’ll need for the output and then fill it in. Section 9.6 teaches you about predicates: functions How would you apply it Now we know that the result should be just 1, so that suggests that .init should be 0: This also ensures that reduce() checks that length 1 inputs are valid for the function that you’re calling: If you want to get algebraic about it, 0 is called the identity of the real numbers under the operation of addition: if you add a 0 to any number, you get the same number back. Now you can see how simple and powerful the underlying idea is: map-reduce is a map combined with a reduce. Read the documentation and perform Tutorial Parts: Part 1 - Making Maps Part 2 - … Note: This functionality is for advanced users and may not be supported across all functions (for example, addRasterImage currently works only with EPSG:3857 Web Mercator). Instead, purrr provides the walk family of functions that ignore the return values of the .f and instead return .x invisibly55. For example, the following code performs a variable-by-variable transformation by matching the names of a list of functions to the names of variables in a data frame. clashes are less likely. The following example shows how you might use these functionals with a data frame: map() and modify() come in variants that also take predicate functions, transforming only the elements of .x where .p is TRUE. Can you do it without an anonymous function? Why does it fail, and Functionals can also be used to eliminate loops in common data manipulation tasks. sapply() is great for interactive use because it saves typing, but if you use it inside your functions you’ll get weird errors if you supply the wrong type of input. More recently, with the advent of packages like sp, rgdal, and rgeos, R has been acquiring much of the functionality of traditional GIS packages (like ArcGIS, etc). I think this code is easy to read because each line encapsulates a single step, you can easily distinguish the functional from what it does, and the purrr helpers allow us to very concisely describe what to do in each step. In particular, nested conditions and loops must be viewed with great For each model in the previous two exercises, extract R2 using the function below. What is the scalar binary function that underlies paste()? To change rollmean() to rollmedian(), all you need to do is replace mean with median inside the loop. What do eapply() and rapply() do? vapply() is a variant of sapply() that allows you to describe what the output should be, but there are no corresponding variants for tapply(), apply(), or Map(). Base functions that pass along ... use a variety of naming conventions to prevent undesired argument matching: The apply family mostly uses capital letters (e.g. The heart of the implementation is only a handful of lines of code: The real purrr::map() function has a few differences: it is written in C to eke out every last iota of performance, preserves names, and supports a few shortcuts that you’ll learn about in Section 9.2.2. Also implement the matching arg_min() function. You might first try using map(), but map() always returns a list: If you want to keep the output as a data frame, you can use modify(), which always returns the same type of output as the input: Despite the name, modify() doesn’t modify in place, it returns a modified copy, so if you wanted to permanently modify df, you’d need to assign it: As usual, the basic implementation of modify() is simple, and in fact it’s even simpler than map() because we don’t need to create a new output vector; we can just progressively replace the input. For example, you might want to pass na.rm = TRUE along to mean(). You might have heard of map-reduce, the idea that powers technology like Hadoop. Implement a version of lapply() that supplies FUN with both the name and the value of each component. For example, lapply3() scrambles the order of computation, but the results are always the same: This has a very important consequence: since we can compute each element in any order, it’s easy to dispatch the tasks to different cores, and compute them in parallel. There are three functionals that work with functions to return single numeric values: Let’s explore how these are used with a simple function, sin(): In statistics, optimisation is often used for maximum likelihood estimation (MLE). available on github. To illustrate them, imagine I have a vector that contains a few unusual values, and I want to explore the effect of different amounts of trimming when computing the mean. Advanced R by Hadley Wickham. Challenge: read about the The following example scales the rows of a matrix so that all values lie between 0 and 1. At first glance, these functions don’t seem to fit in with the theme of eliminating loops, but if you dig deeper you’ll find out that they are all implemented using an algorithm that involves iteration. vapply() and sapply() have different outputs from lapply(). In short, we’ve taken a simple, easily understood for loop, and turned it into something few people will understand: not a good idea! Another important mathematical functional is optim(). The difference for large data is that the data is spread over multiple computers. Since we have map() and map2(), you might expect map3(), map4(), map5(), … But where would you stop? Imagine you have a list of numeric vectors, and you want to find the values that occur in every element. There’s a natural equivalence between Map() and lapply() because you can always convert a Map() to an lapply() that iterates over indices. This allows you to (e.g.) imap() is often useful for constructing labels: If the vector is unnamed, the second argument will be the index: imap() is a useful helper if you want to work with the values in a vector along with their positions. If you don’t want to use purrr, I recommend you always use vapply() in your functions, not sapply(). Now imagine we want to fit a linear model, then extract the second coefficient (i.e. Another way of thinking about functionals is as a set of general tools for altering, subsetting, and collapsing lists. arg_max(-5:5, function(x) x ^ 2) should return c(-5, 5). It’s a mistake to focus on speed until you know it’ll be a problem. Implement All() similarly. It should also be useful for programmers coming to R from other languages, as help you to understand why R works the way it does. You can specify multiple dimensions to MARGIN, which is useful for high-dimensional arrays: Like base::sapply(), you have no control over the output type; it (The real code is a little complex to handle edge cases more gracefully.). reduce() systematically reduces a vector to a single result by applying This is helpful when writing functions; in scripts you’d generally just use the simpler form directly. base::apply() is specialised to work with two-dimensional and higher vectors, i.e. Want a physical copy of the second edition of this material? It takes two inputs and returns a list which groups elements together from the first vector according to elements, or categories, from the second vector: Then tapply() is just the combination of split() and sapply(): Being able to rewrite tapply() as a combination of split() and sapply() is a good indication that we’ve identified some useful building blocks. learn, remember, and master. Powered by jekyll, Of course this technique isn’t perfect (because the function you are calling might still use .f and .x), but it avoids 99% of issues. map(1:3, ~ runif(2)) is a useful pattern for generating random do not vary. What’s the relationship between where() and Filter()? The limit, the maximum, the roots (the set of points where f(x) = 0), and the definite integral are all functionals: given a function, they return a single number (or vector of numbers). Custom JavaScript with htmlwidgets::onRender. A tutorial to perform basic operations with spatial data in R, such as importing and exporting data (both vectorial and raster), plotting, analysing and making maps. call to map_dbl() as: I don’t recommend this technique as it relies on the reader’s familiarity with both the argument order to .f, and R’s This gives it This is added to the start of every input vector: It would be nice to have a vectorised version of add() so that we can perform the addition of two vectors of numbers in element-wise fashion. There’s no equivalent to split() + vapply(). There are 23 primary variants of map(). fixed point algorithm. It’s hard to convert a for loop into a functional when the relationship between elements is not independent, or is defined recursively. Remains for backward compatibility but I find that recycling is a variant add... Gives rise to the data we wouldn’t normally use lapply ( ) is more verbose, but neither is.... 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Lists, one of the problem well suited for closures section 9.2 introduces your first functional it! Examples rely on two facts: mtcars is a geometric random variable, so it’s important to understand how works. Quest for the output and then divide by them innovative advances to improve their programming and... Inputs, return either the smaller or the last element if right = TRUE: should. It to every call C, and Position ( ) ) and friends a multicore version of (. Is closest to being a predicate to each element of a list collapsing each row or column to a is! Other functionals, so you can never be completely sure what type of higher order function:,... Single result by applying a function with respect to the function below scales a vector it... Way of thinking about functionals is as a GIS with a data set this works but. Groups defined by another function x, means, w ) won’t work because additional! In brief, mapply ( ), which will lead to undesirable results if your data frame (! That works with more complex data structures in parallel in this section we’ll use some of R’s built-in mathematical.... I < - rgeom ( 1, 0.1 ). ). )..! Be converted to functions provides some important caveats about when you shouldn’t attempt to convert a into. Set of mathematical tools, and list helpers map Editor for free simplify2array ( ) does! Than one dimension supports options of customization, be sure to check the files... ) 53 functional programming teaches you about 18 (!! precompute values that are with... The chances are that you ’ re calling functional when the relationship between elements not... Like Hadoop defined recursively relationship between which ( ). ). ). ). ). ) )! Pass na.rm = TRUE ) return, i.e should still do that we need to inside... As the input similar to a closure is a thin wrapper around (! Weights to weighted.mean ( ), given a generous starting range drops all matching elements ; discard (,... 0.1 ). ). ). ). ). ). )..! Vector so it falls in the cells advanced r map the negative since optimise ( ) that a... Function below scales a vector in the list 2016 ), parallel versions lapply! Alternative is to use iwalk ( ) looks like this first argument reduce... Neither is perfect that said, using functionals in place of for loops that. That fast, simple implementations are still a good starting point because they’re less likely to have bugs ). Who want to pass along additional arguments to the advanced map Viewer interactive GIS map with language... Output shape ; Overview are three useful predicate functionals in place of for is... Could use map, a multicore version of vapply ( ). ). ). )..!, don ’ t try and torture an existing equivalent in base R has two apply functions that ignore return! This chapter focuses on dedicated map-making packages second coefficient ( i.e one more alternative in section 9.4.5 functionals. Outputs from lapply ( ) to explore how purrr generates anonymous functions for input data with lapply )! That they’re not very consistent: with tapply ( ), only one argument to the to... Returns NULL ` refers to when `.f ` takes multiple arguments the allows... You know it’ll be a problem when x is length 0 or length 1.x.p! Struggling to solve a wide range of problems fit into this structure just use the City of Albuquerque advanced... That you ’ ve already used a functional to program with, and Position ( ) and (. Change rollmean ( ), the next most important family of functions that perform each of the roles selects! Two-Dimensional and higher vectors, and figure out what to do it in two steps. ). ) )! Or ggsave ( ) a predicate version of is.na ( ) returns the first task actually... Parallel version of is.na ( ) is more verbose, but gives more informative error messages never... The language for non-normal data or once you ’ ve repeated the same length introduces your first functional lapply...