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## Make your R simulation models 20 times faster

R can be frustratingly slow if you use its loops. However, you can speed

it up significantly (e.g. 20 times!) using the `Rcpp`

package. That

could turn a day long simulation into an hour long simulation.

I had heard years ago about the `Rcpp`

package. `Rcpp`

lets you write

and use C ++ functions in R. However, I had never bothered to learn how

to write C ++. Instead if my simulation model got too slow, I just

redefined the problem (e.g. by using smaller spatial domain) so I could

continue with R.

I persisted with R, rather than use another language, because of its

powerful graphics and the convenience of using a functional language

like R to perform sensitivity analyses. More on this later.

The other day I was browsing Wickhams Advanced

R book and realised it is actually pretty easy

to write basic C++ loops.

Then I wondered if it would still be faster if you had to make repeated

calls to the same C++ function, for instance if you wanted to run a

sensitivity analysis, varying some model parameters. I like to use R for

this task because the `purrr`

package makes it incredibly easy to run

arbitrary combinations of parameters through a function. Then it is

straightforward to summarize and plot the results with `ggplot2`

.

Turns out you can get a massive improvement, even for repeated calls to

the same function. Here is a test.

### A population model in R

First up, let’s write a simple model for simulating population size over

time, according to the logistic function. The below function just takes

your standard `r`

(intrinsic population growth) and `k`

(carrying

capacity) parameters and simulates population size starting at `yinit`

over `t`

years.

Further, to I have included a stochastic process, whose variation is

controlled by `thetasd`

, to illustrate `Rcpp`

random number generator.

```
logmodr <- function(t, yinit, r, k, thetasd){
y <- numeric(t)
y[1] <- yinit
theta <- rnorm(t, 0, thetasd)
for(i in 2:t){
y[i] <- y[i-1]*(r - r*(y[i-1]/k)) * exp(theta[i])
}
return(y)
}
```

Note that I also ran these models without the stochastic component. The

speedup was even greater when you compared C++ to R without the

stochastic step (about 20 times).

### A population model in C++

Now let’s write the equivalent C++ function. You will need to install

the `Rcpp`

package. Note that it has some other software dependencies,

so I recommend you read the guide on

CRAN.

We write the function definition as a string and pass it to

`cppFunction`

from `Rcpp`

:

```
library(Rcpp)
cppFunction("NumericVector logmodc(int t, double yinit, double r,
double k, double thetasd){
NumericVector y(t);
y[0] = yinit;
NumericVector theta = rnorm(t, 0, thetasd);
for (int i = 1; i < t; ++i){
y[i] = y[i-1]*(r - r*(y[i-1] / k)) * exp(theta[i]);
}
return y;
}
")
```

Hopefully you can understand this, even if you are not familiar with

C++. The syntax is reasonably similar to R. If you learned to program in

R you may notice a few discrepencies.

First, C++ requires that you specify the type of each variable when its

created. You can’t just create new variables without assigning them a

type, and you can’t just change the type. This makes C++ more efficient

than R, because the computer knows exactly how much memory to allocate a

variable and doesn’t have to watch for changes.

Second, notice I start the iterator at time-step `1`

, whereas in the R

code we started at time-step `2`

. In C++ vectors are indexed starting at

`0`

.

Finally, don’t forget to end lines with `;`

(you can use `;`

to end

lines in R, but it is not essential).

### Running a single simulation

First up, we need to define the model parameters:

```
t <- 100
yinit <- 1
k <- 20
thetasd <- 0.1
r <- 0.2
```

Now we can run our model. I am just going to plug the models straight

into `microbenchmark`

, so I can compare their times.

```
library(microbenchmark)
mb1 <- microbenchmark(
logmodc(t, yinit, 1.4, k, thetasd),
logmodr(t, yinit, 1.4, k, thetasd)
)
mb1
## Unit: microseconds
## expr min lq mean median
## logmodc(t, yinit, 1.4, k, thetasd) 10.051 11.1100 12.70373 11.7415
## logmodr(t, yinit, 1.4, k, thetasd) 179.053 198.8315 251.48889 224.3450
## uq max neval cld
## 12.8825 67.801 100 a
## 296.1400 1098.436 100 b
```

So the C++ version is 19 times faster.

### Running multiple simulations

So C++ is faster for a single call to a function (that contains a loop).

No surprises there. What if we want to make repeated calls to the same

function, is C++ still faster than R? We might want to make repeated

calls if we want to run different values of `r`

through our model to do

a sensitivty analysis.

We could increase the scope of the C++ code to include a loop over

different values of `r`

. However, then we would lose some of the

convenience of R, which is good at manipulating data. We also wouldn’t

be able to use `purrr`

package to make sensitivity analysis easy.

First, up let’s create a sequence of `r`

values:

```
rseq <- seq(1.1, 2.2, length.out = 10)
```

Now we can run our two models. I will use `purrr::map`

(the `::`

just

means `map`

is in the package `purrr`

and avoids another call to

`library()`

). We will also use `set.seed()`

to make sure both algorithms

generate the same series of random numbers, that way we can check

whether the results are identical.

```
set.seed(42)
yc <- purrr::map(rseq, ~logmodc(t, yinit, .x, k, thetasd))
set.seed(42)
yr <- purrr::map(rseq, ~logmodr(t, yinit, .x, k, thetasd))
```

`map`

iteratively steps through `rseq`

replacing the `.x`

in the

function call with each value of `r`

in turn. Note that we also have to

turn the function call into a formula (with `~`

) to iterate in this way.

`map`

returns a list, where each element is a time-series of population

sizes for a given value of `r`

.

Let’s plot the result, for the second value of `r`

:

```
plot(yr[[2]], type = "l", col = "DarkBlue", lwd = 2)
points(yc[[2]], pch = 16, col = "Tomato", cex = 0.8)
legend('topleft', legend = c("R solution","C solution"),
pch = 16, col = c("DarkBlue", "Tomato"))
```

They look identical, excellent.

Now, let’s compare the time. Remember I had wondered whether repeated

calls to a C++ function might lose some of the performance gain:

```
mb2 <- microbenchmark(
purrr::map(rseq, ~logmodc(t, yinit, .x, k, thetasd)),
purrr::map(rseq, ~logmodr(t, yinit, .x, k, thetasd))
)
mb2
## Unit: microseconds
## expr min lq
## purrr::map(rseq, ~logmodc(t, yinit, .x, k, thetasd)) 151.421 166.4165
## purrr::map(rseq, ~logmodr(t, yinit, .x, k, thetasd)) 1890.549 2047.6310
## mean median uq max neval cld
## 199.9101 179.5795 221.885 371.192 100 a
## 2543.3459 2233.7455 2534.350 9173.440 100 b
```

Turns out we still gain a 12 times improvement when using C++.

I don’t believe I have been wasting so many hours waiting for

simulations to run all these years. Learning a bit of C++ is well worth

the investment.

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