24 Improving performance
24.1 Introduction
We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%. A good programmer will not be lulled into complacency by such reasoning, he will be wise to look carefully at the critical code; but only after that code has been identified.
— Donald Knuth
Once you’ve used profiling to identify a bottleneck, you need to make it faster. It’s difficult to provide general advice on improving performance, but I try my best with four techniques that can be applied in many situations. I’ll also suggest a general strategy for performance optimisation that helps ensure that your faster code is still correct.
It’s easy to get caught up in trying to remove all bottlenecks. Don’t! Your time is valuable and is better spent analysing your data, not eliminating possible inefficiencies in your code. Be pragmatic: don’t spend hours of your time to save seconds of computer time. To enforce this advice, you should set a goal time for your code and optimise only up to that goal. This means you will not eliminate all bottlenecks. Some you will not get to because you’ve met your goal. Others you may need to pass over and accept either because there is no quick and easy solution or because the code is already well optimised and no significant improvement is possible. Accept these possibilities and move on to the next candidate.
If you’d like to learn more about the performance characteristics of the R language, I’d highly recommend Evaluating the Design of the R Language.^{111} It draws conclusions by combining a modified R interpreter with a wide set of code found in the wild.
Outline
Section 24.2 teaches you how to organise your code to make optimisation as easy, and bug free, as possible.
Section 24.3 reminds you to look for existing solutions.
Section 24.4 emphasises the importance of being lazy: often the easiest way to make a function faster is to let it to do less work.
Section 24.5 concisely defines vectorisation, and shows you how to make the most of builtin functions.
Section 24.6 discusses the performance perils of copying data.
Section 24.7 pulls all the pieces together into a case study showing how to speed up repeated ttests by about a thousand times.
Section 24.8 finishes the chapter with pointers to more resources that will help you write fast code.
24.2 Code organisation
There are two traps that are easy to fall into when trying to make your code faster:
 Writing faster but incorrect code.
 Writing code that you think is faster, but is actually no better.
The strategy outlined below will help you avoid these pitfalls.
When tackling a bottleneck, you’re likely to come up with multiple approaches. Write a function for each approach, encapsulating all relevant behaviour. This makes it easier to check that each approach returns the correct result and to time how long it takes to run. To demonstrate the strategy, I’ll compare two approaches for computing the mean:
I recommend that you keep a record of everything you try, even the failures. If a similar problem occurs in the future, it’ll be useful to see everything you’ve tried. To do this I recommend RMarkdown, which makes it easy to intermingle code with detailed comments and notes.
Next, generate a representative test case. The case should be big enough to capture the essence of your problem but small enough that it only takes a few seconds at most. You don’t want it to take too long because you’ll need to run the test case many times to compare approaches. On the other hand, you don’t want the case to be too small because then results might not scale up to the real problem. Here I’m going to use 100,000 numbers:
x < runif(1e5)
Now use bench::mark()
to precisely compare the variations. bench::mark()
automatically checks that all calls return the same values. This doesn’t guarantee that the function behaves the same for all inputs, so in an ideal world you’ll also have unit tests to make sure you don’t accidentally change the behaviour of the function.
bench::mark(
mean1(x),
mean2(x)
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 2 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 mean1(x) 162µs 176µs 5571.
#> 2 mean2(x) 190µs 202µs 4914.
(You might be surprised by the results: mean(x)
is considerably slower than sum(x) / length(x)
. This is because, among other reasons, mean(x)
makes two passes over the vector to be more numerically accurate.)
If you’d like to see this strategy in action, I’ve used it a few times on stackoverflow:
24.3 Checking for existing solutions
Once you’ve organised your code and captured all the variations you can think of, it’s natural to see what others have done. You are part of a large community, and it’s quite possible that someone has already tackled the same problem. Two good places to start are:
CRAN task views. If there’s a CRAN task view related to your problem domain, it’s worth looking at the packages listed there.
Reverse dependencies of Rcpp, as listed on its CRAN page. Since these packages use C++, they’re likely to be fast.
Otherwise, the challenge is describing your bottleneck in a way that helps you find related problems and solutions. Knowing the name of the problem or its synonyms will make this search much easier. But because you don’t know what it’s called, it’s hard to search for it! The best way to solve this problem is to read widely so that you can build up your own vocabulary over time. Alternatively, ask others. Talk to your colleagues and brainstorm some possible names, then search on Google and StackOverflow. It’s often helpful to restrict your search to R related pages. For Google, try rseek. For stackoverflow, restrict your search by including the R tag, [R]
, in your search.
Record all solutions that you find, not just those that immediately appear to be faster. Some solutions might be slower initially, but end up being faster because they’re easier to optimise. You may also be able to combine the fastest parts from different approaches. If you’ve found a solution that’s fast enough, congratulations! Otherwise, read on.
24.3.1 Exercises
What are faster alternatives to
lm()
? Which are specifically designed to work with larger datasets?What package implements a version of
match()
that’s faster for repeated lookups? How much faster is it?List four functions (not just those in base R) that convert a string into a date time object. What are their strengths and weaknesses?
Which packages provide the ability to compute a rolling mean?
What are the alternatives to
optim()
?
24.4 Doing as little as possible
The easiest way to make a function faster is to let it do less work. One way to do that is use a function tailored to a more specific type of input or output, or to a more specific problem. For example:
rowSums()
,colSums()
,rowMeans()
, andcolMeans()
are faster than equivalent invocations that useapply()
because they are vectorised (Section 24.5).vapply()
is faster thansapply()
because it prespecifies the output type.If you want to see if a vector contains a single value,
any(x == 10)
is much faster than10 %in% x
because testing equality is simpler than testing set inclusion.
Having this knowledge at your fingertips requires knowing that alternative functions exist: you need to have a good vocabulary. Expand your vocab by regularly reading R code. Good places to read code are the Rhelp mailing list and StackOverflow.
Some functions coerce their inputs into a specific type. If your input is not the right type, the function has to do extra work. Instead, look for a function that works with your data as it is, or consider changing the way you store your data. The most common example of this problem is using apply()
on a data frame. apply()
always turns its input into a matrix. Not only is this error prone (because a data frame is more general than a matrix), it is also slower.
Other functions will do less work if you give them more information about the problem. It’s always worthwhile to carefully read the documentation and experiment with different arguments. Some examples that I’ve discovered in the past include:
read.csv()
: specify known column types withcolClasses
. (Also consider switching toreadr::read_csv()
ordata.table::fread()
which are considerably faster thanread.csv()
.)factor()
: specify known levels withlevels
.cut()
: don’t generate labels withlabels = FALSE
if you don’t need them, or, even better, usefindInterval()
as mentioned in the “see also” section of the documentation.unlist(x, use.names = FALSE)
is much faster thanunlist(x)
.interaction()
: if you only need combinations that exist in the data, usedrop = TRUE
.
Below, I explore how you might improve apply this strategy to improve the performance of mean()
and as.data.frame()
.
24.4.1 mean()
Sometimes you can make a function faster by avoiding method dispatch. If you’re calling a method in a tight loop, you can avoid some of the costs by doing the method lookup only once:
For S3, you can do this by calling
generic.class()
instead ofgeneric()
.For S4, you can do this by using
selectMethod()
to find the method, saving it to a variable, and then calling that function.
For example, calling mean.default()
is quite a bit faster than calling mean()
for small vectors:
x < runif(1e2)
bench::mark(
mean(x),
mean.default(x)
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 2 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 mean(x) 4.49µs 5.24µs 182949.
#> 2 mean.default(x) 2.38µs 2.87µs 313818.
This optimisation is a little risky. While mean.default()
is almost twice as fast for 100 values, it will fail in surprising ways if x
is not a numeric vector.
An even riskier optimisation is to directly call the underlying .Internal
function. This is faster because it doesn’t do any input checking or handle NA’s, so you are buying speed at the cost of safety.
x < runif(1e2)
bench::mark(
mean(x),
mean.default(x),
.Internal(mean(x))
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 3 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 mean(x) 4.4µs 5.26µs 182483.
#> 2 mean.default(x) 2.34µs 2.81µs 345913.
#> 3 .Internal(mean(x)) 463ns 550ns 1655842.
NB: Most of these differences arise because x
is small. If you increase the size the differences basically disappear, because most of the time is now spent computing the mean, not finding the underlying implementation. This is a good reminder that the size of the input matters, and you should motivate your optimisations based on realistic data.
x < runif(1e4)
bench::mark(
mean(x),
mean.default(x),
.Internal(mean(x))
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 3 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 mean(x) 21.3µs 23µs 43026.
#> 2 mean.default(x) 18.5µs 20µs 48240.
#> 3 .Internal(mean(x)) 15.8µs 16.8µs 58343.
24.4.2 as.data.frame()
Knowing that you’re dealing with a specific type of input can be another way to write faster code. For example, as.data.frame()
is quite slow because it coerces each element into a data frame and then rbind()
s them together. If you have a named list with vectors of equal length, you can directly transform it into a data frame. In this case, if you can make strong assumptions about your input, you can write a method that’s considerably faster than the default.
quickdf < function(l) {
class(l) < "data.frame"
attr(l, "row.names") < .set_row_names(length(l[[1]]))
l
}
l < lapply(1:26, function(i) runif(1e3))
names(l) < letters
bench::mark(
as.data.frame = as.data.frame(l),
quick_df = quickdf(l)
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 2 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 as.data.frame 1.97ms 2.1ms 471.
#> 2 quick_df 17.18µs 19.4µs 48584.
Again, note the tradeoff. This method is fast because it’s dangerous. If you give it bad inputs, you’ll get a corrupt data frame:
quickdf(list(x = 1, y = 1:2))
#> Warning in format.data.frame(if (omit) x[seq_len(n0), , drop = FALSE] else x, :
#> corrupt data frame: columns will be truncated or padded with NAs
#> x y
#> 1 1 1
To come up with this minimal method, I carefully read through and then rewrote the source code for as.data.frame.list()
and data.frame()
. I made many small changes, each time checking that I hadn’t broken existing behaviour. After several hours work, I was able to isolate the minimal code shown above. This is a very useful technique. Most base R functions are written for flexibility and functionality, not performance. Thus, rewriting for your specific need can often yield substantial improvements. To do this, you’ll need to read the source code. It can be complex and confusing, but don’t give up!
24.4.3 Exercises
What’s the difference between
rowSums()
and.rowSums()
?Make a faster version of
chisq.test()
that only computes the chisquare test statistic when the input is two numeric vectors with no missing values. You can try simplifyingchisq.test()
or by coding from the mathematical definition.Can you make a faster version of
table()
for the case of an input of two integer vectors with no missing values? Can you use it to speed up your chisquare test?
24.5 Vectorise
If you’ve used R for any length of time, you’ve probably heard the admonishment to “vectorise your code”. But what does that actually mean? Vectorising your code is not just about avoiding for loops, although that’s often a step. Vectorising is about taking a wholeobject approach to a problem, thinking about vectors, not scalars. There are two key attributes of a vectorised function:
It makes many problems simpler. Instead of having to think about the components of a vector, you only think about entire vectors.
The loops in a vectorised function are written in C instead of R. Loops in C are much faster because they have much less overhead.
Chapter 9 stressed the importance of vectorised code as a higher level abstraction. Vectorisation is also important for writing fast R code. This doesn’t mean simply using map()
or lapply()
. Instead, vectorisation means finding the existing R function that is implemented in C and most closely applies to your problem.
Vectorised functions that apply to many common performance bottlenecks include:

rowSums()
,colSums()
,rowMeans()
, andcolMeans()
. These vectorised matrix functions will always be faster than usingapply()
. You can sometimes use these functions to build other vectorised functions. Vectorised subsetting can lead to big improvements in speed. Remember the techniques behind lookup tables (Section 4.5.1) and matching and merging by hand (Section 4.5.2). Also remember that you can use subsetting assignment to replace multiple values in a single step. If
x
is a vector, matrix or data frame thenx[is.na(x)] < 0
will replace all missing values with 0.If you’re extracting or replacing values in scattered locations in a matrix or data frame, subset with an integer matrix. See Section 4.2.3 for more details.
If you’re converting continuous values to categorical make sure you know how to use
cut()
andfindInterval()
.
Matrix algebra is a general example of vectorisation. There loops are executed by highly tuned external libraries like BLAS. If you can figure out a way to use matrix algebra to solve your problem, you’ll often get a very fast solution. The ability to solve problems with matrix algebra is a product of experience. A good place to start is to ask people with experience in your domain.
Vectorisation has a downside: it is harder to predict how operations will scale. The following example measures how long it takes to use character subsetting to look up 1, 10, and 100 elements from a list. You might expect that looking up 10 elements would take 10 times as long as looking up 1, and that looking up 100 elements would take 10 times longer again. In fact, the following example shows that it only takes about ~10x longer to look up 100 elements than it does to look up 1. That happens because once you get to a certain size, the internal implementation switches to a strategy that has a higher set up cost, but scales better.
lookup < setNames(as.list(sample(100, 26)), letters)
x1 < "j"
x10 < sample(letters, 10)
x100 < sample(letters, 100, replace = TRUE)
bench::mark(
lookup[x1],
lookup[x10],
lookup[x100],
check = FALSE
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 3 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 lookup[x1] 1.22µs 1.41µs 692473.
#> 2 lookup[x10] 2.38µs 2.61µs 346828.
#> 3 lookup[x100] 5.48µs 7.88µs 124169.
Vectorisation won’t solve every problem, and rather than torturing an existing algorithm into one that uses a vectorised approach, you’re often better off writing your own vectorised function in C++. You’ll learn how to do so in Chapter 25.
24.5.1 Exercises
The density functions, e.g.,
dnorm()
, have a common interface. Which arguments are vectorised over? What doesrnorm(10, mean = 10:1)
do?Compare the speed of
apply(x, 1, sum)
withrowSums(x)
for varying sizes ofx
.How can you use
crossprod()
to compute a weighted sum? How much faster is it than the naivesum(x * w)
?
24.6 Avoiding copies
A pernicious source of slow R code is growing an object with a loop. Whenever you use c()
, append()
, cbind()
, rbind()
, or paste()
to create a bigger object, R must first allocate space for the new object and then copy the old object to its new home. If you’re repeating this many times, like in a for loop, this can be quite expensive. You’ve entered Circle 2 of the R inferno.
You saw one example of this type of problem in Section 23.2.2, so here I’ll show a slightly more complex example of the same basic issue. We first generate some random strings, and then combine them either iteratively with a loop using collapse()
, or in a single pass using paste()
. Note that the performance of collapse()
gets relatively worse as the number of strings grows: combining 100 strings takes almost 30 times longer than combining 10 strings.
random_string < function() {
paste(sample(letters, 50, replace = TRUE), collapse = "")
}
strings10 < replicate(10, random_string())
strings100 < replicate(100, random_string())
collapse < function(xs) {
out < ""
for (x in xs) {
out < paste0(out, x)
}
out
}
bench::mark(
loop10 = collapse(strings10),
loop100 = collapse(strings100),
vec10 = paste(strings10, collapse = ""),
vec100 = paste(strings100, collapse = ""),
check = FALSE
)[c("expression", "min", "median", "itr/sec", "n_gc")]
#> # A tibble: 4 x 4
#> expression min median `itr/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl>
#> 1 loop10 47.54µs 52.3µs 18752.
#> 2 loop100 890.07µs 946.1µs 1053.
#> 3 vec10 9.47µs 10.5µs 91693.
#> 4 vec100 42.26µs 45.4µs 21767.
Modifying an object in a loop, e.g., x[i] < y
, can also create a copy, depending on the class of x
. Section 2.5.1 discusses this issue in more depth and gives you some tools to determine when you’re making copies.
24.7 Case study: ttest
The following case study shows how to make ttests faster using some of the techniques described above. It’s based on an example in Computing thousands of test statistics simultaneously in R by Holger Schwender and Tina Müller. I thoroughly recommend reading the paper in full to see the same idea applied to other tests.
Imagine we have run 1000 experiments (rows), each of which collects data on 50 individuals (columns). The first 25 individuals in each experiment are assigned to group 1 and the rest to group 2. We’ll first generate some random data to represent this problem:
m < 1000
n < 50
X < matrix(rnorm(m * n, mean = 10, sd = 3), nrow = m)
grp < rep(1:2, each = n / 2)
For data in this form, there are two ways to use t.test()
. We can either use the formula interface or provide two vectors, one for each group. Timing reveals that the formula interface is considerably slower.
system.time(
for (i in 1:m) {
t.test(X[i, ] ~ grp)$statistic
}
)
#> user system elapsed
#> 0.859 0.004 0.864
system.time(
for (i in 1:m) {
t.test(X[i, grp == 1], X[i, grp == 2])$statistic
}
)
#> user system elapsed
#> 0.237 0.000 0.238
Of course, a for loop computes, but doesn’t save the values. We can map_dbl()
(Section 9.2.1) to do that. This adds a little overhead:
compT < function(i){
t.test(X[i, grp == 1], X[i, grp == 2])$statistic
}
system.time(t1 < purrr::map_dbl(1:m, compT))
#> user system elapsed
#> 0.250 0.003 0.252
How can we make this faster? First, we could try doing less work. If you look at the source code of stats:::t.test.default()
, you’ll see that it does a lot more than just compute the tstatistic. It also computes the pvalue and formats the output for printing. We can try to make our code faster by stripping out those pieces.
my_t < function(x, grp) {
t_stat < function(x) {
m < mean(x)
n < length(x)
var < sum((x  m) ^ 2) / (n  1)
list(m = m, n = n, var = var)
}
g1 < t_stat(x[grp == 1])
g2 < t_stat(x[grp == 2])
se_total < sqrt(g1$var / g1$n + g2$var / g2$n)
(g1$m  g2$m) / se_total
}
system.time(t2 < purrr::map_dbl(1:m, ~ my_t(X[.,], grp)))
#> user system elapsed
#> 0.041 0.000 0.040
stopifnot(all.equal(t1, t2))
This gives us about a sixfold speed improvement.
Now that we have a fairly simple function, we can make it faster still by vectorising it. Instead of looping over the array outside the function, we will modify t_stat()
to work with a matrix of values. Thus, mean()
becomes rowMeans()
, length()
becomes ncol()
, and sum()
becomes rowSums()
. The rest of the code stays the same.
rowtstat < function(X, grp){
t_stat < function(X) {
m < rowMeans(X)
n < ncol(X)
var < rowSums((X  m) ^ 2) / (n  1)
list(m = m, n = n, var = var)
}
g1 < t_stat(X[, grp == 1])
g2 < t_stat(X[, grp == 2])
se_total < sqrt(g1$var / g1$n + g2$var / g2$n)
(g1$m  g2$m) / se_total
}
system.time(t3 < rowtstat(X, grp))
#> user system elapsed
#> 0.015 0.001 0.014
stopifnot(all.equal(t1, t3))
That’s much faster! It’s at least 40 times faster than our previous effort, and around 1000 times faster than where we started.
24.8 Other techniques
Being able to write fast R code is part of being a good R programmer. Beyond the specific hints in this chapter, if you want to write fast R code, you’ll need to improve your general programming skills. Some ways to do this are to:
Read R blogs to see what performance problems other people have struggled with, and how they have made their code faster.
Read other R programming books, like The Art of R Programming^{112} or Patrick Burns’ R Inferno to learn about common traps.
Take an algorithms and data structure course to learn some well known ways of tackling certain classes of problems. I have heard good things about Princeton’s Algorithms course offered on Coursera.
Learn how to parallelise your code. Two places to start are Parallel R^{113} and Parallel Computing for Data Science.^{114}
Read general books about optimisation like Mature optimisation^{115} or the Pragmatic Programmer.^{116}
You can also reach out to the community for help. StackOverflow can be a useful resource. You’ll need to put some effort into creating an easily digestible example that also captures the salient features of your problem. If your example is too complex, few people will have the time and motivation to attempt a solution. If it’s too simple, you’ll get answers that solve the toy problem but not the real problem. If you also try to answer questions on StackOverflow, you’ll quickly get a feel for what makes a good question.