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I've been learning R for a while now, and have come across a lot of advice to programming types like myself to vectorize operations. Being a programmer, I'm interested as to why / how it's faster. An example: n = 10^7 # populate with random nos v=runif(n) system.time({vv<-v*v; m<-mean(vv)}); m system.time({for(i in 1:length(v)) { vv[i]<-v[i]*v[i] }; m<-mean(vv)}); m This gave user system elapsed 0.04 0.01 0.07 [1] 0.3332091 user system elapsed 36.68 0.02 36.69 [1] 0.3332091 The most obvious thing to consider is that we're running native code, i.e. machine code compiled from C or C++, rather than interpreted code, as shown by the massive difference in user time between the two examples (circa 3 orders of magnitude). But is there anything else going on? For example, does R do: Cunning native data structures, e.g. clever ways of storing sparse vectors or matrices so that we only do multiplications when we need to? Lazy evaluation, e.g. on a matrix multiply, don't evaluate cells until as and when you need to. Parallel processing. Something else. To test whether there might be some sparse vector optimization I tried doing dot products with difference vector contents # populate with random nos v<-runif(n) system.time({m<-v%*%v/n}); m # populate with runs of 1 followed by 99 0s v <-rep(rep(c(1,rep(0,99)),n/100)) system.time({m<-v%*%v/n}); m # populate with 0s v <-rep(0,n) system.time({m<-v%*%v/n}); m However there was no significant difference in time (circa 0.09 elapsed) (Similar question for Matlab: Why does vectorized code run faster than for loops in MATLAB? )

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