sequence of a rolling average in Clojure

Question

I'm looking for an elegant way to generate a sequence of the rolling average of a sequence of numbers. Hopefully something more elegant than using lazy-seq

Answer 1

There's a very similar question on SO: Calculating the Moving Average of a List. It's more general -- a number of FP-friendly languages are represented, with the accepted answer using Scala -- but there are a few nice Clojure solutions.

I've posted my own solution over there. Note that it does use lazy-seq, but that's because I wanted it to perform well for large periods (which means adjusting the average at each step rather than calculating a separate average for each window of size = period into the input list). Look around that Q for nice solutions which made the other tradeoff, resulting in shorter code with a somewhat more declarative feel, which actually performs better for very short periods (although suffers significant slowdowns for longer periods, as is to be expected).

Answer 2

Without any consideration of efficiency:

(defn average [lst] (/ (reduce + lst) (count lst)))

(defn moving-average [window lst] (map average (partition window 1 lst)))


user> (moving-average 5 '(1 2 3 4 5 6 7 8))
(3 4 5 6)

If you need it to be fast, there are some fairly obvious improvements to be made! But it will get less elegant.

Answer 3

This version is a bit faster, especially for long windows, since it keeps a rolling sum and avoids repeatedly adding the same things.

Because of the lazy-seq, it's also perfectly general and won't blow stack

(defn partialsums [start lst]
  (lazy-seq
    (if-let [lst (seq lst)] 
          (cons start (partialsums (+ start (first lst)) (rest lst)))
          (list start))))

(defn sliding-window-moving-average [window lst]
  (map #(/ % window)
       (let [start   (apply + (take window lst))
             diffseq (map - (drop window lst) lst)]
         (partialsums start diffseq))))

;; To help see what it's doing:

(sliding-window-moving-average 5 '(1 2 3 4 5 6 7 8 9 10 11))

start = (+ 1 2 3 4 5) = 15

diffseq = - (6 7 8 9 10 11)
            (1 2 3 4  5  6 7 8 9 10 11)

        =   (5 5 5 5  5  5)

(partialsums 15 '(5 5 5 5 5 5) ) = (15 20 25 30 35 40 45)

(map #(/ % 5) (20 25 30 35 40 45)) = (3 4 5 6 7 8 9)

;; Example

(take 20 (sliding-window-moving-average 5 (iterate inc 0)))