Measure the periodicity of a sequence of numbers [R]

Question

A periodic sequence is a sequence that repeats itself after n terms, for example, the following is a periodic sequence:

1, 2, 3, 1, 2, 3, 1, 2, 3, ...

And we define the period of that sequence to be the number of terms in each subsequence (the subsequence above is 1, 2, 3). So the period for the above sequence is 3.

In R, I can define the above sequence (albeit not to infinity), using:

sequence <- rep(c(1,2,3),n) #n is a predefined variable

So if n = 50, sequence will be the sequence 1, 2, 3, 1, 2, 3, ... , 1, 2, 3, where each number has appeared 50 times, in the obvious way.

I am looking to build a function that calculates the periodicity of sequence. Pseudocode is as follows:

period <- function(sequence){
    subsequence <- subsequence(sequence) #identify the subsequence
    len.subsequence <- length(subsequence) #calculate its length
    return(len.subsequence) #return it
}

How would I identify the subsequence? This is sort of a reversing of the rep function, such that I pass in a sequence and it passes out the length of the initial vector.

Answer 1

If the period is always the same, i.e. the sequence never changes, then you could use a loop over lag to see when a match occurs.

With total bias, I would also recommend using seqle (guess who wrote that function :-) ), which is like rle but finds sequences. detect intervals of the consequent integer sequences I'm not the only person to edit the source for "rle" that way.

Answer 2

It's fairly easy with that sequence, although I would avoid using the name 'sequence' since it is an R function name. This would identify the periodicity of any monotonic sequence so it's a bit more general but it would not identify a sequence like: 1.2.3.4.2.3.4,1,2,3,4,2,3,4, ....

> which(diff(seQ) < 0)
[1]  3  6  9 12 15 18 21 24 27
> diff(which(diff(seQ) < 0) )
[1] 3 3 3 3 3 3 3 3

You could test the equality of intervals or use either of those results to index the original vector. You should test your answers with c(1, 2, 3, 4, 2, 3, 4, 1, 2, 3, 4, 2, 3, 4) to see if they pass the test of identifying an non-monotonic repetition. So far none of them do so; since none report a period of 7.