Perf-improve.Rmd

# Improving performance {#perf-improve}

```{r, include = FALSE}
source("common.R")
```

## Introduction
\index{performance!improving}

> 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_ [@r-design]. It draws conclusions by combining a modified R interpreter with a wide set of code found in the wild.

### Outline {-}

* Section \@ref(code-organisation) teaches you how to organise 
  your code to make optimisation as easy, and bug free, as possible.

* Section \@ref(already-solved) reminds you to look for existing
  solutions.

* Section \@ref(be-lazy) emphasises the importance of
  being lazy: often the easiest way to make a function faster is to 
  let it to do less work.

* Section \@ref(vectorise) concisely defines vectorisation, and shows you
  how to make the most of built-in functions.

* Section \@ref(avoid-copies) discusses the performance perils of 
  copying data. 

* Section \@ref(t-test) pulls all the pieces together into a case
  study showing how to speed up repeated t-tests by about a thousand times. 

* Section \@ref(more-techniques) finishes the chapter with pointers to
  more resources that will help you write fast code.

### Prerequisites {-}

We'll use [bench](https://bench.r-lib.org/) to precisely compare the performance of small self-contained code chunks.

```{r setup}
library(bench)
```

## Code organisation {#code-organisation}
\index{performance!strategy}

There are two traps that are easy to fall into when trying to make your code faster:

1. Writing faster but incorrect code.
1. 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:

```{r}
mean1 <- function(x) mean(x)
mean2 <- function(x) sum(x) / length(x)
```

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:

```{r}
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.

```{r}
bench::mark(
  mean1(x),
  mean2(x)
)[c("expression", "min", "median", "itr/sec", "n_gc")]
```

(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:

* <http://stackoverflow.com/questions/22515525#22518603>
* <http://stackoverflow.com/questions/22515175#22515856>
* <http://stackoverflow.com/questions/3476015#22511936>

## Checking for existing solutions {#already-solved}

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](http://cran.rstudio.com/web/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](http://cran.r-project.org/web/packages/Rcpp). 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](http://www.rseek.org/). 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.

### Exercises

1.  What are faster alternatives to `lm()`? Which are specifically designed 
    to work with larger datasets?

1.  What package implements a version of `match()` that's faster for
    repeated lookups? How much faster is it?

1.  List four functions (not just those in base R) that convert a string into a
    date time object. What are their strengths and weaknesses?

1.  Which packages provide the ability to compute a rolling mean?

1.  What are the alternatives to `optim()`?

## Doing as little as possible {#be-lazy}

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()`, and `colMeans()` are faster than
  equivalent invocations that use `apply()` because they are vectorised 
  (Section \@ref(vectorise)).

* `vapply()` is faster than `sapply()` because it pre-specifies the output
  type.

* If you want to see if a vector contains a single value, `any(x == 10)`
  is much faster than `10 %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 [R-help mailing list](https://stat.ethz.ch/mailman/listinfo/r-help) and [StackOverflow](http://stackoverflow.com/questions/tagged/r).

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 with `colClasses`. (Also consider
  switching to `readr::read_csv()` or `data.table::fread()` which are 
  considerably faster than `read.csv()`.)

* `factor()`: specify known levels with `levels`.

* `cut()`: don't generate labels with `labels = FALSE` if you don't need them,
  or, even better, use `findInterval()` as mentioned in the "see also" section
  of the documentation.
  
* `unlist(x, use.names = FALSE)` is much faster than `unlist(x)`.

* `interaction()`: if you only need combinations that exist in the data, use
  `drop = TRUE`.

Below, I explore how you might improve apply this strategy to improve the performance of `mean()` and `as.data.frame()`.

### `mean()`
\indexc{.Internal()}
\index{method dispatch!performance}

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 of `generic()`. 

* 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:

```{r}
x <- runif(1e2)

bench::mark(
  mean(x),
  mean.default(x)
)[c("expression", "min", "median", "itr/sec", "n_gc")]
```

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.

```{r}
x <- runif(1e2)
bench::mark(
  mean(x),
  mean.default(x),
  .Internal(mean(x))
)[c("expression", "min", "median", "itr/sec", "n_gc")]
```

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.

```{r}
x <- runif(1e4)
bench::mark(
  mean(x),
  mean.default(x),
  .Internal(mean(x))
)[c("expression", "min", "median", "itr/sec", "n_gc")]
```


### `as.data.frame()`
\indexc{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.

```{r}
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")]
```

Again, note the trade-off. This method is fast because it's dangerous. If you give it bad inputs, you'll get a corrupt data frame:

```{r}
quickdf(list(x = 1, y = 1:2))
```

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!

### Exercises

1.  What's the difference between `rowSums()` and `.rowSums()`?

1.  Make a faster version of `chisq.test()` that only computes the chi-square
    test statistic when the input is two numeric vectors with no missing
    values. You can try simplifying `chisq.test()` or by coding from the 
    [mathematical definition](http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test).

1.  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 chi-square test?

## Vectorise {#vectorise}
\index{vectorisation}

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 whole-object 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 \@ref(functionals) 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()`, and `colMeans()`. These vectorised 
  matrix functions will always be faster than using `apply()`. You can
  sometimes use these functions to build other vectorised functions. 
  
    ```{r}
    rowAny <- function(x) rowSums(x) > 0
    rowAll <- function(x) rowSums(x) == ncol(x)
    ```
    
* Vectorised subsetting can lead to big improvements in speed. Remember the 
  techniques behind lookup tables (Section \@ref(lookup-tables)) and matching 
  and merging by hand (Section \@ref(matching-merging)). 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 then 
  `x[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 \@ref(matrix-subsetting) for more details.

* If you're converting continuous values to categorical make sure you know
  how to use `cut()` and `findInterval()`.

* Be aware of vectorised functions like `cumsum()` and `diff()`.

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.

```{r}
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")]
```

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 \@ref(rcpp). 

### Exercises

1.  The density functions, e.g., `dnorm()`, have a common interface. Which 
    arguments are vectorised over? What does `rnorm(10, mean = 10:1)` do?

1.  Compare the speed of `apply(x, 1, sum)` with `rowSums(x)` for varying sizes
    of `x`.
  
1.  How can you use `crossprod()` to compute a weighted sum? How much faster is
    it than the naive `sum(x * w)`?

## Avoiding copies {#avoid-copies}
\index{loops!avoiding copies in}
\indexc{paste()}

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_](http://www.burns-stat.com/pages/Tutor/R_inferno.pdf). 

You saw one example of this type of problem in Section \@ref(memory-profiling), 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.

```{r}
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")]
```

Modifying an object in a loop, e.g., `x[i] <- y`, can also create a copy, depending on the class of `x`. Section \@ref(single-binding) discusses this issue in more depth and gives you some tools to determine when you're making copies.

## Case study: t-test {#t-test}

The following case study shows how to make t-tests faster using some of the techniques described above. It's based on an example in [_Computing thousands of test statistics simultaneously in R_](http://stat-computing.org/newsletter/issues/scgn-18-1.pdf) 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:

```{r}
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.

```{r, cache = TRUE}
system.time(
  for (i in 1:m) {
    t.test(X[i, ] ~ grp)$statistic
  }
)
system.time(
  for (i in 1:m) {
    t.test(X[i, grp == 1], X[i, grp == 2])$statistic
  }
)
```

Of course, a for loop computes, but doesn't save the values. We can `map_dbl()` (Section \@ref(map-atomic)) to do that. This adds a little overhead:

```{r}
compT <- function(i){
  t.test(X[i, grp == 1], X[i, grp == 2])$statistic
}
system.time(t1 <- purrr::map_dbl(1:m, compT))
```

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 t-statistic. It also computes the p-value and formats the output for printing. We can try to make our code faster by stripping out those pieces.

```{r}
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)))
stopifnot(all.equal(t1, t2))
```

This gives us about a six-fold 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.

```{r}
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))
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.

<!-- These timing comparisons are not reflected in the code. In the pdf copy this last function takes 0.011 s while the original version takes 0.191 s (about 17 times slower). Maybe there was improvement in the base version of t.test? -->

## Other techniques {#more-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](http://www.r-bloggers.com/) 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_ 
  [@art-r-prog] or Patrick Burns'
  [_R Inferno_](http://www.burns-stat.com/documents/books/the-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](https://www.coursera.org/course/algs4partI) offered on
  Coursera.
  
* Learn how to parallelise your code. Two places to start are
  _Parallel R_ [@parallel-r] and _Parallel Computing for Data Science_
  [@parcomp-ds].

* Read general books about optimisation like _Mature optimisation_ [@mature-opt]
  or the _Pragmatic Programmer_ [@pragprog].
  
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.