Wednesday, April 6, 2011

Speeding up R computations

The past few days I've been going through some R code that I wrote last year, when I was preparing a massive simulation-based power study for some tests for multivariate normality that I've been working on. My goal was to reduce the time needed to run the simulation. I wasn't expecting great improvement, since I've always believed that the most common R functions are properly vectorized and optimized for speed. Turns out I was wrong. Very wrong.

The first thing that I did was that I replaced all parentheses ( ) by curly brackets { }. I was inspired to do so by this post (and this, via Xi'Ans Og) over at Radford Neal's blog. As he pointed out, code that uses parentheses is actually slower than the same code with curly brackets:

> system.time( for(i in 1:1000000) { 1*(1+1) } )
   user  system elapsed 
  1.337   0.005   1.349 
> system.time( for(i in 1:1000000) { 1*{1+1} } )
   user  system elapsed 
  1.072   0.003   1.076 

Similarly, you can compare a*a and a^2:

> system.time( for(i in 1:10000000) 3^2 )
   user  system elapsed 
  5.048   0.028   5.088 
> system.time( for(i in 1:10000000) 3*3 )
   user  system elapsed 
  4.721   0.024   4.748 

So, a^2 is slower than a*a. This made me wonder, are there other built-in R functions that are slower than they ought to be?

One thing that I found very surprising, and frankly rather disturbing, is that mean(x) takes ten times as long to calculate the mean value of the 50 real numbers in the vector x as the "manual" function sum(x)/50:

> x<-rnorm(50)
> system.time(for(i in 1:100000){mean(x)})
   user  system elapsed 
  1.522   0.000   1.523 
> system.time(for(i in 1:100000){sum(x)/length(x)})
   user  system elapsed 
  0.200   0.000   0.200 
> system.time(for(i in 1:100000){sum(x)/50})
   user  system elapsed 
  0.167   0.000   0.167 
> system.time(for(i in 1:100000){ overn<-rep(1/50,50); x%*%overn })
   user  system elapsed 
  0.678   0.000   0.677 
> overn<-rep(1/50,50); system.time(for(i in 1:100000){ x%*%overn })
   user  system elapsed 
  0.164   0.000   0.164 

I guess that the R development core team have been focusing on making R an easy-to-use high level programming language rather than optimizing all functions, but the poor performance of mean is just embarrassing.

Similarly, the var function can be greatly improved upon. Here are some of the many possibilites:

> x <- rnorm(50)
> system.time( for(i in 1:100000) { var(x) } )
   user  system elapsed 
  4.921   0.000   4.925 
> system.time( for(i in 1:100000) { sum((x-mean(x))^2)/{length(x)-1} } )
   user  system elapsed 
  2.322   0.000   2.325 
> system.time( for(i in 1:100000) { {sum(x*x)-sum(x)*sum(x)/length(x)}/{length(x)-1} } )
   user  system elapsed 
  0.736   0.000   0.737 
> system.time( for(i in 1:100000) { {sum(x*x)-sum(x)*sum(x)/50}/49 } )
   user  system elapsed 
  0.618   0.000   0.618 

> system.time( for(i in 1:100000) { sx<-sum(x); {sum(x*x)-sx*sx/50}/49 } )
   user  system elapsed 
  0.567   0.000   0.568

I changed all the uses of mean in my code to "sum/n" instead (and avoided using var entirely) and found that this sped things up quite a bit.

Another trick to speed up your computations is to create the vectors that you wish to change within a loop with the right number of elements. While

for(j in 1:100) a[j]<-j 

works just fine, it is actually quite a bit slower than

for(j in 1:100) a[j]<-j

You could create a in other ways as well of course, for instance by a<-vector(length=100). Here are the numbers:

> system.time( for(i in 1:100000) { a<-NA; for(j in 1:100) a[j]<-j })
   user  system elapsed 
 37.383   0.092  37.482 
> system.time( for(i in 1:100000) { a<-rep(NA,100); for(j in 1:100) a[j]<-j })
   user  system elapsed 
 25.866   0.065  25.936 
> system.time( for(i in 1:100000) { a<-vector(length=100); for(j in 1:100) a[j]<-j })
   user  system elapsed 
 25.517   0.022  25.548

In my case, I'd been a bit sloppy with creating the vectors in my loops in the proper way, so I changed this in my code as well.

In my simulation study, I simulate multivariate random variables, compute some test statistics and use these to estimate the powers of the normality tests against various alternatives. After doing the changes mentioned above, I compared the performance of my old code to that of the new code, for 1000 iterations of the procedure:

> system.time( source("oldCode.R") )
   user  system elapsed 
548.045   0.273 548.622 
> system.time( source("newCode.R") )
   user  system elapsed 
 93.138   0.002  93.194

The improved code is almost 6 times faster than the old code. When you do ten million or so iterations, that matters. A lot.

In conclusion, it's definitely possible to speed up your code significantly if you know of the pitfalls of R. I suspect that I'll be obsessed with finding more pitfalls in the next few weeks, so I'd be thankful for any hints about other weaknesses that R has.

It should probably be mentioned that R is really fast when things are properly vectorized. Last year, a coworker that uses Matlab challenged me to perform a number of matrix computations faster in R than in Matlab. To his great surprise, R won.

As a final remark, I'm now facing a bit of a dilemma. Should I write readable code; a^6; or fast code; a*a*a*a*a*a?

Update: looking to speed up your R computations even more? See my posts on compiling your code and parallelization.