The R Book

Looking for runs of numbers within vectors

The function is called rle, which stands for ‘run length encoding’ and is most easily understood with an example. Here is a vector of 150 random numbers from a Poisson distribution with mean 0.7:

(poisson<-rpois(150,0.7))

  [1]     1     1     0     0     2     1     0     1     0     1     0     0     0     0     2     1     0     0     3     1
          0     0     1     0     2     0     1     1     0     0     0     1     0     0     0     2     1
 [38]     0     0     0     1     0     0     0     2     0     0     0     1     1     0     2     1     0     0     0     2
          0     0     2     3     2     1     0     2     0     0     0     0     0     1     1     0     0
 [75]     0     0     0     1     1     1     0     0     1     0     1     2     2     0     0     2     0     0     0     0
[112]     0     0     2     0     0     1     0     1     0     4     0     0     1     0     2     1     0     1     1     0
          0     1     3     3     0     0     1     1     0     1     0     0     0     0     0     1     0
[149]     2     0

We can do our own run length encoding on the vector by eye: there is a run of two 1s, then a run of two 0s, then a single 2, then a single 1, then a single 0, and so on. So the run lengths are 2, 2, 1, 1, 1, 1, . . . . The values associated with these runs were 1, 0, 2, 1, 0, 1,. Here is the output from rle:

rle(poisson)

Run Length Encoding
lengths:  int [1:93] 2 2 1 1 1 1 1 1 4 1...
values :  num [1:93] 1 0 2 1 0 1 0 1 0 2...

The object produced by rle is a list of two vectors: the lengths and the values. To find the longest run, and the value associated with that longest run, we use the indexed lists like this:

max(rle(poisson)[[1]])

[1] 7

So the longest run in this vector of numbers was 7. But 7 of what? We use which to find the location of the 7 in lengths, then apply this index to values to find the answer:

which(rle(poisson)[[1]]==7)

[1]  55

rle(poisson)[[2]][55]

[1]  0

So, not surprisingly given that the mean was just 0.7, ...