Averages/Simple moving average
You are encouraged to solve this task according to the task description, using any language you may know.
Computing the simple moving average of a series of numbers.
The task is to:
- Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period. It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
- The period, P
- An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudocode for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also: Standard Deviation
Ada
moving.ads: <lang Ada>generic
Max_Elements : Positive; type Number is digits <>;
package Moving is
procedure Add_Number (N : Number); function Moving_Average (N : Number) return Number; function Get_Average return Number;
end Moving;</lang>
moving.adb: <lang Ada>with Ada.Containers.Vectors;
package body Moving is
use Ada.Containers;
package Number_Vectors is new Ada.Containers.Vectors
(Element_Type => Number,
Index_Type => Natural);
Current_List : Number_Vectors.Vector := Number_Vectors.Empty_Vector;
procedure Add_Number (N : Number) is
begin
if Natural (Current_List.Length) >= Max_Elements then
Current_List.Delete_First;
end if;
Current_List.Append (N);
end Add_Number;
function Get_Average return Number is
Average : Number := 0.0;
procedure Sum (Position : Number_Vectors.Cursor) is
begin
Average := Average + Number_Vectors.Element (Position);
end Sum;
begin
Current_List.Iterate (Sum'Access);
if Current_List.Length > 1 then
Average := Average / Number (Current_List.Length);
end if;
return Average;
end Get_Average;
function Moving_Average (N : Number) return Number is
begin
Add_Number (N);
return Get_Average;
end Moving_Average;
end Moving;</lang>
main.adb: <lang Ada>with Ada.Text_IO; with Moving; procedure Main is
package Three_Average is new Moving (Max_Elements => 3, Number => Float); package Five_Average is new Moving (Max_Elements => 5, Number => Float);
begin
for I in 1 .. 5 loop
Ada.Text_IO.Put_Line ("Inserting" & Integer'Image (I) &
" into max-3: " & Float'Image (Three_Average.Moving_Average (Float (I))));
Ada.Text_IO.Put_Line ("Inserting" & Integer'Image (I) &
" into max-5: " & Float'Image (Five_Average.Moving_Average (Float (I))));
end loop;
for I in reverse 1 .. 5 loop
Ada.Text_IO.Put_Line ("Inserting" & Integer'Image (I) &
" into max-3: " & Float'Image (Three_Average.Moving_Average (Float (I))));
Ada.Text_IO.Put_Line ("Inserting" & Integer'Image (I) &
" into max-5: " & Float'Image (Five_Average.Moving_Average (Float (I))));
end loop;
end Main;</lang>
Output:
Inserting 1 into max-3: 1.00000E+00 Inserting 1 into max-5: 1.00000E+00 Inserting 2 into max-3: 1.50000E+00 Inserting 2 into max-5: 1.50000E+00 Inserting 3 into max-3: 2.00000E+00 Inserting 3 into max-5: 2.00000E+00 Inserting 4 into max-3: 3.00000E+00 Inserting 4 into max-5: 2.50000E+00 Inserting 5 into max-3: 4.00000E+00 Inserting 5 into max-5: 3.00000E+00 Inserting 5 into max-3: 4.66667E+00 Inserting 5 into max-5: 3.80000E+00 Inserting 4 into max-3: 4.66667E+00 Inserting 4 into max-5: 4.20000E+00 Inserting 3 into max-3: 4.00000E+00 Inserting 3 into max-5: 4.20000E+00 Inserting 2 into max-3: 3.00000E+00 Inserting 2 into max-5: 3.80000E+00 Inserting 1 into max-3: 2.00000E+00 Inserting 1 into max-5: 3.00000E+00
ALGOL 68
Note: This following code is a direct translation of the C code sample. It mimics C's var_list implementation, and so it probably isn't the most natural way of dong this actual task in ALGOL 68. <lang Algol68>MODE SMAOBJ = STRUCT(
LONG REAL sma, LONG REAL sum, INT period, REF[]LONG REAL values, INT lv
);
MODE SMARESULT = UNION (
REF SMAOBJ # handle #, LONG REAL # sma #, REF[]LONG REAL # values #
);
MODE SMANEW = INT,
SMAFREE = STRUCT(REF SMAOBJ free obj),
SMAVALUES = STRUCT(REF SMAOBJ values obj),
SMAADD = STRUCT(REF SMAOBJ add obj, LONG REAL v),
SMAMEAN = STRUCT(REF SMAOBJ mean obj, REF[]LONG REAL v);
MODE ACTION = UNION ( SMANEW, SMAFREE, SMAVALUES, SMAADD, SMAMEAN );
PROC sma = ([]ACTION action)SMARESULT: (
SMARESULT result; REF SMAOBJ obj; LONG REAL v;
FOR i FROM LWB action TO UPB action DO
CASE action[i] IN
(SMANEW period):( # args: INT period #
HEAP SMAOBJ handle;
sma OF handle := 0.0;
period OF handle := period;
values OF handle := HEAP [period OF handle]LONG REAL;
lv OF handle := 0;
sum OF handle := 0.0;
result := handle
),
(SMAFREE args):( # args: REF SMAOBJ free obj #
free obj OF args := REF SMAOBJ(NIL) # let the garbage collector do it's job #
),
(SMAVALUES args):( # args: REF SMAOBJ values obj #
result := values OF values obj OF args
),
(SMAMEAN args):( # args: REF SMAOBJ mean obj #
result := sma OF mean obj OF args
),
(SMAADD args):( # args: REF SMAOBJ add obj, LONG REAL v #
obj := add obj OF args;
v := v OF args;
IF lv OF obj < period OF obj THEN
(values OF obj)[lv OF obj+:=1] := v;
sum OF obj +:= v;
sma OF obj := sum OF obj / lv OF obj
ELSE
sum OF obj -:= (values OF obj)[ 1+ lv OF obj MOD period OF obj];
sum OF obj +:= v;
sma OF obj := sum OF obj / period OF obj;
(values OF obj)[ 1+ lv OF obj MOD period OF obj ] := v; lv OF obj+:=1
FI;
result := sma OF obj
)
OUT
SKIP
ESAC
OD;
result
);
[]LONG REAL v = ( 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 );
main: (
INT i;
REF SMAOBJ h3 := ( sma(SMANEW(3)) | (REF SMAOBJ obj):obj );
REF SMAOBJ h5 := ( sma(SMANEW(5)) | (REF SMAOBJ obj):obj );
FOR i FROM LWB v TO UPB v DO
printf(($"next number "g(0,6)", SMA_3 = "g(0,6)", SMA_5 = "g(0,6)l$,
v[i], (sma(SMAADD(h3, v[i]))|(LONG REAL r):r), ( sma(SMAADD(h5, v[i])) | (LONG REAL r):r )
))
OD#;
sma(SMAFREE(h3));
sma(SMAFREE(h5))
)</lang>Output:
next number 1.000000, SMA_3 = 1.000000, SMA_5 = 1.000000 next number 2.000000, SMA_3 = 1.500000, SMA_5 = 1.500000 next number 3.000000, SMA_3 = 2.000000, SMA_5 = 2.000000 next number 4.000000, SMA_3 = 3.000000, SMA_5 = 2.500000 next number 5.000000, SMA_3 = 4.000000, SMA_5 = 3.000000 next number 5.000000, SMA_3 = 4.666667, SMA_5 = 3.800000 next number 4.000000, SMA_3 = 4.666667, SMA_5 = 4.200000 next number 3.000000, SMA_3 = 4.000000, SMA_5 = 4.200000 next number 2.000000, SMA_3 = 3.000000, SMA_5 = 3.800000 next number 1.000000, SMA_3 = 2.000000, SMA_5 = 3.000000
AutoHotkey
ahk forum: discussion For Integers: <lang AutoHotkey>MsgBox % MovingAverage(5,3) ; 5, averaging length <- 3 MsgBox % MovingAverage(1) ; 3 MsgBox % MovingAverage(-3) ; 1 MsgBox % MovingAverage(8) ; 2 MsgBox % MovingAverage(7) ; 4
MovingAverage(x,len="") { ; for integers (faster)
Static
Static sum:=0, n:=0, m:=10 ; default averaging length = 10
If (len>"") ; non-blank 2nd parameter: set length, reset
sum := n := i := 0, m := len
If (n < m) ; until the buffer is not full
sum += x, n++ ; keep summing data
Else ; when buffer is full
sum += x-v%i% ; add new, subtract oldest
v%i% := x, i := mod(i+1,m) ; remember last m inputs, cycle insertion point
Return sum/n
}</lang> For floating point numbers: <lang AutoHotkey>MovingAverage(x,len="") { ; for floating point numbers
Static
Static n:=0, m:=10 ; default averaging length = 10
If (len>"") ; non-blank 2nd parameter: set length, reset
n := i := 0, m := len
n += n < m, sum := 0
v%i% := x, i := mod(i+1,m) ; remember last m inputs, cycle insertion point
Loop %n% ; recompute sum to avoid error accumulation
j := A_Index-1, sum += v%j%
Return sum/n
}</lang>
AWK
<lang awk>#!/usr/bin/awk -f
- Moving average over the first column of a data file
BEGIN {
P = 5;
}
{
x = $1; i = NR % P; MA += (x - Z[i]) / P; Z[i] = x; print MA;
}</lang>
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <stdarg.h>
typedef struct sma_obj {
double sma; double sum; int period; double *values; int lv;
} sma_obj_t;
typedef union sma_result {
sma_obj_t *handle; double sma; double *values;
} sma_result_t;
enum Action { SMA_NEW, SMA_FREE, SMA_VALUES, SMA_ADD, SMA_MEAN }; sma_result_t sma(enum Action action, ...) {
va_list vl; sma_result_t r; sma_obj_t *o; double v;
va_start(vl, action);
switch(action) {
case SMA_NEW: // args: int period
r.handle = malloc(sizeof(sma_obj_t));
r.handle->sma = 0.0;
r.handle->period = va_arg(vl, int);
r.handle->values = malloc(r.handle->period * sizeof(double));
r.handle->lv = 0;
r.handle->sum = 0.0;
break;
case SMA_FREE: // args: sma_obj_t *handle
r.handle = va_arg(vl, sma_obj_t *);
free(r.handle->values);
free(r.handle);
r.handle = NULL;
break;
case SMA_VALUES: // args: sma_obj_t *handle
o = va_arg(vl, sma_obj_t *);
r.values = o->values;
break;
case SMA_MEAN: // args: sma_obj_t *handle
o = va_arg(vl, sma_obj_t *);
r.sma = o->sma;
break;
case SMA_ADD: // args: sma_obj_t *handle, double value
o = va_arg(vl, sma_obj_t *);
v = va_arg(vl, double);
if ( o->lv < o->period ) {
o->values[o->lv++] = v;
o->sum += v;
o->sma = o->sum / o->lv;
} else {
o->sum -= o->values[ o->lv % o->period];
o->sum += v;
o->sma = o->sum / o->period;
o->values[ o->lv % o->period ] = v; o->lv++;
}
r.sma = o->sma;
break;
}
va_end(vl);
return r;
}</lang>
<lang c>double v[] = { 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 };
int main() {
int i;
sma_obj_t *h3 = sma(SMA_NEW, 3).handle; sma_obj_t *h5 = sma(SMA_NEW, 5).handle;
for(i=0; i < sizeof(v)/sizeof(double) ; i++) {
printf("next number %lf, SMA_3 = %lf, SMA_5 = %lf\n",
v[i], sma(SMA_ADD, h3, v[i]).sma, sma(SMA_ADD, h5, v[i]).sma);
}
sma(SMA_FREE, h3); sma(SMA_FREE, h5); return 0;
}</lang>
C++
<lang cpp>
- include <iostream>
- include <stddef.h>
- include <assert.h>
using std::cout; using std::endl;
class SMA { public: SMA(unsigned int period) : period(period), window(new double[period]), head(NULL), tail(NULL), total(0) { assert(period >= 1); } ~SMA() { delete[] window; }
// Adds a value to the average, pushing one out if nescessary void add(double val) { // Special case: Initialization if (head == NULL) { head = window; *head = val; tail = head; inc(tail); total = val; return; }
// Were we already full? if (head == tail) { // Fix total-cache total -= *head; // Make room inc(head); }
// Write the value in the next spot. *tail = val; inc(tail);
// Update our total-cache total += val; }
// Returns the average of the last P elements added to this SMA. // If no elements have been added yet, returns 0.0 double avg() const { ptrdiff_t size = this->size(); if (size == 0) { return 0; // No entries => 0 average } return total / (double) size; // Cast to double for floating point arithmetic }
private: unsigned int period; double * window; // Holds the values to calculate the average of.
// Logically, head is before tail double * head; // Points at the oldest element we've stored. double * tail; // Points at the newest element we've stored.
double total; // Cache the total so we don't sum everything each time.
// Bumps the given pointer up by one. // Wraps to the start of the array if needed. void inc(double * & p) { if (++p >= window + period) { p = window; } }
// Returns how many numbers we have stored. ptrdiff_t size() const { if (head == NULL) return 0; if (head == tail) return period; return (period + tail - head) % period; } };
int main(int argc, char * * argv) { SMA foo(3); SMA bar(5);
int data[] = { 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 }; for (int * itr = data; itr < data + 10; itr++) { foo.add(*itr); cout << "Added " << *itr << " avg: " << foo.avg() << endl; } cout << endl; for (int * itr = data; itr < data + 10; itr++) { bar.add(*itr); cout << "Added " << *itr << " avg: " << bar.avg() << endl; }
return 0; } </lang>
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace SMA {
class Program {
static void Main(string[] args) {
var nums = Enumerable.Range(1, 5).Select(n => (double)n);
nums = nums.Concat(nums.Reverse());
var sma3 = SMA(3);
var sma5 = SMA(5);
foreach (var n in nums) {
Console.WriteLine("{0} (sma3) {1,-16} (sma5) {2,-16}", n, sma3(n), sma5(n));
}
}
static Func<double, double> SMA(int p) {
Queue<double> s = new Queue<double>(p);
return (x) => {
if (s.Count >= p) {
s.Dequeue();
}
s.Enqueue(x);
return s.Average();
};
}
}
}</lang>
Output:
1 (sma3) 1 (sma5) 1 2 (sma3) 1.5 (sma5) 1.5 3 (sma3) 2 (sma5) 2 4 (sma3) 3 (sma5) 2.5 5 (sma3) 4 (sma5) 3 5 (sma3) 4.66666666666667 (sma5) 3.8 4 (sma3) 4.66666666666667 (sma5) 4.2 3 (sma3) 4 (sma5) 4.2 2 (sma3) 3 (sma5) 3.8 1 (sma3) 2 (sma5) 3
Clojure
This version uses a persistent queue to hold the most recent p values. Each function returned from init-moving-average has its state in an atom holding a queue value. <lang clojure>(import '[clojure.lang PersistentQueue])
(defn enqueue-max [q p n]
(let [q (conj q n)] (if (<= (count q) p) q (pop q))))
(defn avg [coll] (/ (reduce + coll) (count coll)))
(defn init-moving-avg [p]
(let [state (atom PersistentQueue/EMPTY)]
(fn [n]
(avg (swap! state enqueue-max p n)))))</lang>
CoffeeScript
<lang coffeescript> I = (P) ->
# The cryptic name "I" follows the problem description;
# it returns a function that computes a moving average
# of successive values over the period P, using closure
# variables to maintain state.
cq = circular_queue(P)
num_elems = 0
sum = 0
SMA = (n) ->
sum += n
if num_elems < P
cq.add(n)
num_elems += 1
sum / num_elems
else
old = cq.replace(n)
sum -= old
sum / P
circular_queue = (n) ->
# queue that only ever stores up to n values; # Caller shouldn't call replace until n values # have been added. i = 0 arr = [] add: (elem) -> arr.push elem replace: (elem) -> # return value whose age is "n" old_val = arr[i] arr[i] = elem i = (i + 1) % n old_val
- The output of the code below should convince you that
- calling I multiple times returns functions with independent
- state.
sma3 = I(3) sma7 = I(7) sma11 = I(11) for i in [1..10]
console.log i, sma3(i), sma7(i), sma11(i)
</lang> output <lang> > coffee moving_average.coffee 1 1 1 1 2 1.5 1.5 1.5 3 2 2 2 4 3 2.5 2.5 5 4 3 3 6 5 3.5 3.5 7 6 4 4 8 7 5 4.5 9 8 6 5 10 9 7 5.5 </lang>
Common Lisp
This implementation uses a circular list to store the numbers within the window; at the beginning of each iteration pointer refers to the list cell which holds the value just moving out of the window and to be replaced with the just-added value.
<lang lisp>(defun simple-moving-average (period &aux
(sum 0) (count 0) (values (make-list period)) (pointer values))
(setf (rest (last values)) values) ; construct circularity
(lambda (n)
(when (first pointer)
(decf sum (first pointer))) ; subtract old value
(incf sum n) ; add new value
(incf count)
(setf (first pointer) n)
(setf pointer (rest pointer)) ; advance pointer
(/ sum (min count period))))</lang>
D
Using a Closure
<lang d>import std.stdio, std.traits, std.algorithm;
auto sma(T, int period)() {
T[period] data = 0; // D FP are default-initialized to NaN T sum = 0; int index, nfilled;
// return (in T v) nothrow {
return delegate (in T v) nothrow {
sum += -data[index] + v;
data[index] = v;
index = (index + 1) % period;
nfilled = min(period, nfilled + 1);
return cast(CommonType!(T, float))sum / nfilled;
};
}
void main() {
auto s3 = sma!(int, 3)(); auto s5 = sma!(double, 5)();
foreach (e; [1, 2, 3, 4, 5, 5, 4, 3, 2, 1])
writefln("Added %d, sma(3) = %f, sma(5) = %f",
e, s3(e), s5(e));
}</lang>
- Output:
Added 1, sma(3) = 1.000000, sma(5) = 1.000000 Added 2, sma(3) = 1.500000, sma(5) = 1.500000 Added 3, sma(3) = 2.000000, sma(5) = 2.000000 Added 4, sma(3) = 3.000000, sma(5) = 2.500000 Added 5, sma(3) = 4.000000, sma(5) = 3.000000 Added 5, sma(3) = 4.666667, sma(5) = 3.800000 Added 4, sma(3) = 4.666667, sma(5) = 4.200000 Added 3, sma(3) = 4.000000, sma(5) = 4.200000 Added 2, sma(3) = 3.000000, sma(5) = 3.800000 Added 1, sma(3) = 2.000000, sma(5) = 3.000000
Using a Struct
This version avoids the heap allocation of the closure, same output: <lang d>import std.stdio, std.traits, std.algorithm;
struct SMA(T, int period) {
T[period] data = 0; T sum = 0; int index, nfilled;
auto opCall(in T v) pure nothrow {
sum += -data[index] + v;
data[index] = v;
index = (index + 1) % period;
nfilled = min(period, nfilled + 1);
return cast(CommonType!(T, float))sum / nfilled;
}
}
void main() {
SMA!(int, 3) s3; SMA!(double, 5) s5;
foreach (e; [1, 2, 3, 4, 5, 5, 4, 3, 2, 1])
writefln("Added %d, sma(3) = %f, sma(5) = %f",
e, s3(e), s5(e));
}</lang> To avoid the floating point approximations keep piling up and growing, the code may perform a periodic sum on the whole circular queue array.
E
This implementation produces two (function) objects sharing state. It is idiomatic in E to separate input from output (read from write) rather than combining them into one object.
The structure is the same as the implementation of Standard Deviation#E.
<lang e>pragma.enable("accumulator") def makeMovingAverage(period) {
def values := ([null] * period).diverge()
var index := 0
var count := 0
def insert(v) {
values[index] := v
index := (index + 1) %% period
count += 1
}
/** Returns the simple moving average of the inputs so far, or null if there
have been no inputs. */
def average() {
if (count > 0) {
return accum 0 for x :notNull in values { _ + x } / count.min(period)
}
}
return [insert, average]
}</lang>
> def [insert, average] := makeMovingAverage(period) > println(`Period $period:`) > for value in [1,2,3,4,5,5,4,3,2,1] { > insert(value) > println(value, "\t", average()) > } > println() > }
Period 3: 1 1.0 2 1.5 3 2.0 4 3.0 5 4.0 5 4.666666666666667 4 4.666666666666667 3 4.0 2 3.0 1 2.0
Period 5: 1 1.0 2 1.5 3 2.0 4 2.5 5 3.0 5 3.8 4 4.2 3 4.2 2 3.8
1 3.0</lang>Elena
<lang elena>#define std'dictionary'*.
- define std'basic'*.
- define std'collections'*.
- define std'patterns'*.
- symbol SMA : aPeriod = List~
{
+ aNumber
[
self += NewInt32Value::aNumber.
#if (self count > aPeriod)?
[
self delete &first_item.
].
#var aCount := self count.
#if (aCount == 0)?
[ ^ 0. ].
#var aSum := Real::0.
Scan::self run:anItem => (aSum += anItem).
^ aSum / aCount.
]
}.
- symbol Program =>
[
#var SMA3 := SMA::3.
#var SMA5 := SMA::5.
#var anAction := N =>
[
'program'output << "sma3 + " << N << " = " << SMA3 + N.
'program'output << ",sma5 + " << N << " = " << SMA5 + N << "%n".
].
loop::{ &for:1 &to:5 } run:anAction rewind:anAction.
]. </lang>
F#
<lang fsharp>let sma period f (list:float list) =
let sma_aux queue v =
let q = Seq.truncate period (v :: queue)
Seq.average q, Seq.toList q
List.fold (fun s v ->
let avg,state = sma_aux s v
f avg
state) [] list
printf "sma3: " [ 1.;2.;3.;4.;5.;5.;4.;3.;2.;1.] |> sma 3 (printf "%.2f ") printf "\nsma5: " [ 1.;2.;3.;4.;5.;5.;4.;3.;2.;1.] |> sma 5 (printf "%.2f ") printfn ""</lang>
Output:
sma3: 1.00 1.50 2.00 3.00 4.00 4.67 4.67 4.00 3.00 2.00 sma5: 1.00 1.50 2.00 2.50 3.00 3.80 4.20 4.20 3.80 3.00
Fantom
<lang fantom> class MovingAverage {
Int period
Int[] stream
new make (Int period)
{
this.period = period
stream = [,]
}
// add number to end of stream and remove numbers from start if
// stream is larger than period
public Void addNumber (Int number)
{
stream.add (number)
while (stream.size > period)
{
stream.removeAt (0)
}
}
// compute average of numbers in stream
public Float average ()
{
if (stream.isEmpty)
return 0.0f
else
1.0f * (Int)(stream.reduce(0, |a,b| { (Int) a + b })) / stream.size
}
}
class Main {
public static Void main ()
{ // test by adding random numbers and printing average after each number
av := MovingAverage (5)
10.times |i|
{
echo ("After $i numbers list is ${av.stream} average is ${av.average}")
av.addNumber (Int.random(0..100))
}
}
} </lang>
Sample output for a period of 5:
After 0 numbers list is [,] average is 0.0 After 1 numbers list is [64] average is 64.0 After 2 numbers list is [64, 50] average is 57.0 After 3 numbers list is [64, 50, 26] average is 46.666666666666664 After 4 numbers list is [64, 50, 26, 77] average is 54.25 After 5 numbers list is [64, 50, 26, 77, 82] average is 59.8 After 6 numbers list is [50, 26, 77, 82, 95] average is 66.0 After 7 numbers list is [26, 77, 82, 95, 11] average is 58.2 After 8 numbers list is [77, 82, 95, 11, 23] average is 57.6 After 9 numbers list is [82, 95, 11, 23, 50] average is 52.2
Forth
<lang forth>: f+! ( f addr -- ) dup f@ f+ f! ;
- ,f0s ( n -- ) falign 0 do 0e f, loop ;
- period @ ;
- used cell+ ;
- head 2 cells + ;
- sum 3 cells + faligned ;
- ring ( addr -- faddr )
dup sum float+ swap head @ floats + ;
- update ( fvalue addr -- addr )
dup ring f@ fnegate dup sum f+! fdup dup ring f! dup sum f+! dup head @ 1+ over period mod over head ! ;
- moving-average
create ( period -- ) dup , 0 , 0 , 1+ ,f0s does> ( fvalue -- avg ) update dup used @ over period < if 1 over used +! then dup sum f@ used @ 0 d>f f/ ;
3 moving-average sma 1e sma f. \ 1. 2e sma f. \ 1.5 3e sma f. \ 2. 4e sma f. \ 3.</lang>
Fortran
<lang fortran>program Movavg
implicit none
integer :: i
write (*, "(a)") "SIMPLE MOVING AVERAGE: PERIOD = 3"
do i = 1, 5 write (*, "(a, i2, a, f8.6)") "Next number:", i, " sma = ", sma(real(i)) end do do i = 5, 1, -1 write (*, "(a, i2, a, f8.6)") "Next number:", i, " sma = ", sma(real(i)) end do
contains
function sma(n)
real :: sma real, intent(in) :: n real, save :: a(3) = 0 integer, save :: count = 0
if (count < 3) then count = count + 1 a(count) = n else a = eoshift(a, 1, n) end if
sma = sum(a(1:count)) / real(count)
end function
end program Movavg</lang>
GAP
<lang gap>MovingAverage := function(n)
local sma, buffer, pos, sum, len; buffer := List([1 .. n], i -> 0); pos := 0; len := 0; sum := 0; sma := function(x) pos := RemInt(pos, n) + 1; sum := sum + x - buffer[pos]; buffer[pos] := x; len := Minimum(len + 1, n); return sum/len; end; return sma;
end;
f := MovingAverage(3); f(1); # 1 f(2); # 3/2 f(3); # 2 f(4); # 3 f(5); # 4 f(5); # 14/3 f(4); # 14/3 f(3); # 4 f(2); # 3 f(1); # 2</lang>
Go
<lang go>package main
import "fmt"
func sma(n int) func(float64) float64 {
s := make([]float64, 0, n)
i, sum, rn := 0, 0., 1/float64(n)
return func(x float64) float64 {
if len(s) < n {
sum += x
s = append(s, x)
return sum / float64(len(s))
}
s[i] = x
i++
if i == n {
i = 0
}
sum = 0
for _, x = range s {
sum += x
}
return sum * rn
}
}
func main() {
sma3 := sma(3)
sma5 := sma(5)
fmt.Println("x sma3 sma5")
for _, x := range []float64{1, 2, 3, 4, 5, 5, 4, 3, 2, 1} {
fmt.Printf("%5.3f %5.3f %5.3f\n", x, sma3(x), sma5(x))
}
}</lang> Output:
x sma3 sma5 1.000 1.000 1.000 2.000 1.500 1.500 3.000 2.000 2.000 4.000 3.000 2.500 5.000 4.000 3.000 5.000 4.667 3.800 4.000 4.667 4.200 3.000 4.000 4.200 2.000 3.000 3.800 1.000 2.000 3.000
Groovy
<lang groovy>def simple_moving_average = { size ->
def nums = []
double total = 0.0
return { newElement ->
nums += newElement
oldestElement = nums.size() > size ? nums.remove(0) : 0
total += newElement - oldestElement
total / nums.size()
}
}
ma5 = simple_moving_average(5)
(1..5).each{ printf( "%1.1f ", ma5(it)) } (5..1).each{ printf( "%1.1f ", ma5(it)) }</lang> Sample output:
1.0 1.5 2.0 2.5 3.0 3.8 4.2 4.2 3.8 3.0
Haskell
<lang Haskell>import Data.List import Control.Arrow import Control.Monad
sMA p = map (head *** head ).tail.
scanl (\(y,_) -> (id &&& return. av) . (: if length y == p then init y else y)) ([],[]) where av = liftM2 (/) sum (fromIntegral.length)
printSMA n p = mapM_ (\(n,a) -> putStrLn $ "Next number: " ++ show n ++ " Average: " ++ show a)
. take n . sMA p $ [1..5]++[5,4..1]++[3..]</lang>
Output:
*Main> sequence_ [putStrLn "Moving Average Period 3:",printSMA 10 3 ,putStrLn "\nMoving Average Period 5:",printSMA 10 5] Moving Average Period 3: Next number: 1.0 Average: 1.0 Next number: 2.0 Average: 1.5 Next number: 3.0 Average: 2.0 Next number: 4.0 Average: 3.0 Next number: 5.0 Average: 4.0 Next number: 5.0 Average: 4.666666666666667 Next number: 4.0 Average: 4.666666666666667 Next number: 3.0 Average: 4.0 Next number: 2.0 Average: 3.0 Next number: 1.0 Average: 2.0 Moving Average Period 5: Next number: 1.0 Average: 1.0 Next number: 2.0 Average: 1.5 Next number: 3.0 Average: 2.0 Next number: 4.0 Average: 2.5 Next number: 5.0 Average: 3.0 Next number: 5.0 Average: 3.8 Next number: 4.0 Average: 4.2 Next number: 3.0 Average: 4.2 Next number: 2.0 Average: 3.8 Next number: 1.0 Average: 3.0
HicEst
<lang HicEst>REAL :: n=10, nums(n)
nums = (1,2,3,4,5, 5,4,3,2,1) DO i = 1, n
WRITE() "num=", i, "SMA3=", SMA(3,nums(i)), "SMA5=",SMA(5,nums(i))
ENDDO
END ! of "main"
FUNCTION SMA(period, num) ! maxID independent streams
REAL :: maxID=10, now(maxID), Periods(maxID), Offsets(maxID), Pool(1000)
ID = INDEX(Periods, period)
IF( ID == 0) THEN ! initialization
IDs = IDs + 1
ID = IDs
Offsets(ID) = SUM(Periods) + 1
Periods(ID) = period
ENDIF
now(ID) = now(ID) + 1 ALIAS(Pool,Offsets(ID), Past,Periods(ID)) ! renames relevant part of data pool Past = Past($+1) ! shift left Past(Periods(ID)) = num SMA = SUM(Past) / MIN( now(ID), Periods(ID) ) END</lang>
num=1 SMA3=1 SMA5=1 num=2 SMA3=1.5 SMA5=1.5 num=3 SMA3=2 SMA5=2 num=4 SMA3=3 SMA5=2.5 num=5 SMA3=4 SMA5=3 num=6 SMA3=4.666666667 SMA5=3.8 num=7 SMA3=4.666666667 SMA5=4.2 num=8 SMA3=4 SMA5=4.2 num=9 SMA3=3 SMA5=3.8 num=10 SMA3=2 SMA5=3
Icon and Unicon
<lang unicon>procedure main(A)
sma := buildSMA(3) # Use better name than "I". every write(sma(!A))
end
procedure buildSMA(P)
local stream
c := create {
stream := []
while n := (avg@&source)[1] do {
put(stream, n)
if *stream > P then pop(stream)
every (avg := 0.0) +:= !stream
avg := avg/*stream
}
}
return (@c, c)
end</lang> Note: This program uses Unicon specific co-expression calling syntax. It can be easily modified to run under Icon.
and a sample run:
->ravg 3 1 4 1 5 9 2 6 3 8 3.0 2.0 2.666666666666667 2.0 3.333333333333333 5.0 5.333333333333333 5.666666666666667 3.666666666666667 5.666666666666667 ->
If the Utils package is imported from the Unicon code library then a (Unicon only) solution is:
<lang Unicon>import Utils
procedure main(A)
sma1 := closure(SMA,[],3) sma2 := closure(SMA,[],4) every every n := !A do write(left(sma1(n),20), sma2(n))
end
procedure SMA(stream,P,n)
put(stream, n) if *stream > P then pop(stream) every (avg := 0.0) +:= !stream return avg / *stream
end</lang>
with the sample run:
->ravg 3 1 4 1 5 9 2 6 3 8 3.0 3.0 2.0 2.0 2.666666666666667 2.666666666666667 2.0 2.25 3.333333333333333 2.75 5.0 4.75 5.333333333333333 4.25 5.666666666666667 5.5 3.666666666666667 5.0 5.666666666666667 4.75 ->
J
Note: J is block-oriented, not stream oriented. That is, J expresses algorithms with the semantics that all the data is available at once (rather than maintaining state and waiting for the next item).
In that context, moving average is expressed very concisely in J as (+/%#)\, though it is worth noting that this approach does not provide averages for the initial cases where not all data would be available yet:
<lang J> 5 (+/%#)\ 1 2 3 4 5 5 4 3 2 1 NB. not a solution for this task 3 3.8 4.2 4.2 3.8 3</lang>
In the context of the task, we need to produce a stateful function to consume streams. Since J does not have native lexical closure, we need to implement it. Thus the streaming solution is more complex: <lang j> lex =: 1 :'(a[n__a=.m#_.[a=.18!:3$~0)&(4 :(+/%#)(#~1-128!:5)n__x=.1|.!.y n__x)'</lang> Example: <lang j> sma =: 5 lex
sma&> 1 2 3 4 5 5 4 3 2 1
1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3</lang>
Here, the &> is analogous to the "for each" of other languages.
Or, a more traditional approach could be used:
<lang j>avg=: +/ % # SEQ=: moveAvg=:4 :0"0
SEQ=:SEQ,y
avg ({.~ x -@<. #) SEQ
)
5 moveAvg 1 2 3 4 5 5 4 3 2 1
1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3</lang>
Java
<lang java5>import java.util.LinkedList; import java.util.Queue; public class MovingAverage {
private final Queue<Double> window = new LinkedList<Double>(); private final int period; private double sum;
public MovingAverage(int period) {
assert period > 0 : "Period must be a positive integer";
this.period = period;
}
public void newNum(double num) {
sum += num;
window.add(num);
if (window.size() > period) {
sum -= window.remove();
}
}
public double getAvg() {
if (window.isEmpty()) return 0; // technically the average is undefined
return sum / window.size();
}
public static void main(String[] args) {
double[] testData = {1,2,3,4,5,5,4,3,2,1};
int[] windowSizes = {3,5};
for (int windSize : windowSizes) {
MovingAverage ma = new MovingAverage(windSize);
for (double x : testData) {
ma.newNum(x);
System.out.println("Next number = " + x + ", SMA = " + ma.getAvg());
}
System.out.println();
}
}
}</lang> Output:
Next number = 1.0, SMA = 1.0 Next number = 2.0, SMA = 1.5 Next number = 3.0, SMA = 2.0 Next number = 4.0, SMA = 3.0 Next number = 5.0, SMA = 4.0 Next number = 5.0, SMA = 4.666666666666667 Next number = 4.0, SMA = 4.666666666666667 Next number = 3.0, SMA = 4.0 Next number = 2.0, SMA = 3.0 Next number = 1.0, SMA = 2.0 Next number = 1.0, SMA = 1.0 Next number = 2.0, SMA = 1.5 Next number = 3.0, SMA = 2.0 Next number = 4.0, SMA = 2.5 Next number = 5.0, SMA = 3.0 Next number = 5.0, SMA = 3.8 Next number = 4.0, SMA = 4.2 Next number = 3.0, SMA = 4.2 Next number = 2.0, SMA = 3.8 Next number = 1.0, SMA = 3.0
JavaScript
<lang javascript>function simple_moving_averager(period) {
var nums = [];
return function(num) {
nums.push(num);
if (nums.length > period)
nums.splice(0,1); // remove the first element of the array
var sum = 0;
for (var i in nums)
sum += nums[i];
var n = period;
if (nums.length < period)
n = nums.length;
return(sum/n);
}
}
var sma3 = simple_moving_averager(3); var sma5 = simple_moving_averager(5); var data = [1,2,3,4,5,5,4,3,2,1]; for (var i in data) {
var n = data[i];
// using WSH
WScript.Echo("Next number = " + n + ", SMA_3 = " + sma3(n) + ", SMA_5 = " + sma5(n));
}</lang> output:
Next number = 1, SMA_3 = 1, SMA_5 = 1 Next number = 2, SMA_3 = 1.5, SMA_5 = 1.5 Next number = 3, SMA_3 = 2, SMA_5 = 2 Next number = 4, SMA_3 = 3, SMA_5 = 2.5 Next number = 5, SMA_3 = 4, SMA_5 = 3 Next number = 5, SMA_3 = 4.666666666666667, SMA_5 = 3.8 Next number = 4, SMA_3 = 4.666666666666667, SMA_5 = 4.2 Next number = 3, SMA_3 = 4, SMA_5 = 4.2 Next number = 2, SMA_3 = 3, SMA_5 = 3.8 Next number = 1, SMA_3 = 2, SMA_5 = 3
Liberty BASIC
The interesting thing here is how to implement an equivalent of a stateful function. For sample output see http://libertybasic.conforums.com/index.cgi?board=open&action=display&num=1322956720 <lang lb>
dim v$( 100) ' Each array term stores a particular SMA of period p in p*10 bytes
nomainwin
WindowWidth =1080 WindowHeight = 780
graphicbox #w.gb1, 20, 20, 1000, 700
open "Running averages to smooth data" for window as #w
#w "trapclose quit"
#w.gb1 "down"
old.x = 0 old.y.orig =500 ' black old.y.3.SMA =350 ' red old.y.20.SMA =300 ' green
for i =0 to 999 step 1
scan
v =1.1 +sin( i /1000 *2 *3.14159265) + 0.2 *rnd( 1) ' sin wave with added random noise
x =i /6.28318 *1000
y.orig =500 -v /2.5 *500
#w.gb1 "color black ; down ; line "; i-1; " "; old.y.orig; " "; i; " "; y.orig; " ; up"
y.3.SMA =500 -SMA( 1, v, 3) /2.5 *500 ' SMA given ID of 1 is to do 3-term running average
#w.gb1 "color red ; down ; line "; i-1; " "; old.y.3.SMA +50; " "; i; " "; y.3.SMA +50; " ; up"
y.20.SMA =500 -SMA( 2, v, 20) /2.5 *500 ' SMA given ID of 2 is to do 20-term running average
#w.gb1 "color green ; down ; line "; i-1; " "; old.y.20.SMA +100; " "; i; " "; y.20.SMA +100; " ; up"
'print "Supplied with "; v; ", so SMAs are now "; using( "###.###", SMA( 1, v, 3)); " over 3 terms or "; using( "###.###", SMA( 2, v, 5)) ; " over 5 terms." ' ID, latest data, period
old.y.orig =y.orig
old.y.3.SMA =y.3.SMA
old.y.20.SMA =y.20.SMA
next i
wait
sub quit j$
close #w end
end sub
function SMA( ID, Number, Period)
v$( ID) =right$( " " +str$( Number), 10) +v$( ID) ' add new number at left, lose last number on right
v$( ID) =left$( v$( ID), Period *10)
'print "{"; v$( ID); "}",
k =0 ' number of terms read total =0 ' sum of terms read
do
p$ =mid$( v$( ID), 1 +k *10, 10)
if p$ ="" then exit do
vv =val( p$)
total =total +vv
k =k +1
loop until p$ =""
if k <Period then SMA =total / k else SMA =total /Period
end function </lang>
Logo
Although Logo does not support closures, some varieties of Logo support enough metaprogramming to accomplish this task.
UCB Logo has a DEFINE primitive to construct functions from structured instruction lists. In addition, UCB Logo supports a compact template syntax for quoting lists (backquote "`") and replacing components of quoted lists (comma ","). These facilities can be used together in order to create templated function-defining-functions.
<lang logo>to average :l
output quotient apply "sum :l count :l
end
to make.sma :name :period
localmake "qn word :name ".queue make :qn [] define :name `[ [n] ; parameter list [if equal? count :,:qn ,:period [ignore dequeue ",:qn]] [queue ",:qn :n] [output average :,:qn] ]
end
make.sma "avg3 3
show map "avg3 [1 2 3 4 5] ; [1 1.5 2 3 4]
show text "avg3 ; examine what substitutions took place [[n] [if equal? count :avg3.queue 3 [ignore dequeue "avg3.queue]] [queue "avg3.queue :n] [output average :avg3.queue]]
- the internal queue is in the global namespace, easy to inspect
show :avg3.queue ; [3 4 5]</lang>
If namespace pollution is a concern, UCB Logo supplies a GENSYM command to obtain unique names in order to avoid collisions.
<lang logo> ...
localmake "qn word :name gensym ...
- list user-defined functions and variables
show procedures ; [average avg3 make.sma] show names ; [[[] [avg3.g1]]</lang>
Lua
<lang lua>do
local t = {}
function f(a, b, ...) if b then return f(a+b, ...) else return a end end
function average(n)
if #t == 10 then table.remove(t, 1) end
t[#t + 1] = n
return f(unpack(t)) / #t
end
end for v=1,30 do print(average(v)) end</lang>
OCaml
<lang ocaml>let sma (n, s, q) x =
let l = Queue.length q and s = s +. x in Queue.push x q; if l < n then (n, s, q), s /. float (l + 1) else ( let s = s -. Queue.pop q in (n, s, q), s /. float l )
let _ =
let periodLst = [ 3; 5 ] in
let series = [ 1.; 2.; 3.; 4.; 5.; 5.; 4.; 3.; 2.; 1. ] in
List.iter (fun d ->
Printf.printf "SIMPLE MOVING AVERAGE: PERIOD = %d\n" d;
ignore (
List.fold_left (fun o x ->
let o, m = sma o x in Printf.printf "Next number = %-2g, SMA = %g\n" x m; o
) (d, 0., Queue.create ()) series; ); print_newline (); ) periodLst</lang>
Output:
SIMPLE MOVING AVERAGE: PERIOD = 3 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 3 Next number = 5 , SMA = 4 Next number = 5 , SMA = 4.66667 Next number = 4 , SMA = 4.66667 Next number = 3 , SMA = 4 Next number = 2 , SMA = 3 Next number = 1 , SMA = 2 SIMPLE MOVING AVERAGE: PERIOD = 5 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 2.5 Next number = 5 , SMA = 3 Next number = 5 , SMA = 3.8 Next number = 4 , SMA = 4.2 Next number = 3 , SMA = 4.2 Next number = 2 , SMA = 3.8 Next number = 1 , SMA = 3
More imperatively: <lang ocaml>let sma_create period =
let q = Queue.create ()
and sum = ref 0.0 in
fun x ->
sum := !sum +. x;
Queue.push x q;
if Queue.length q > period then
sum := !sum -. Queue.pop q;
!sum /. float (Queue.length q)
let () =
let periodLst = [ 3; 5 ] in
let series = [ 1.; 2.; 3.; 4.; 5.; 5.; 4.; 3.; 2.; 1. ] in
List.iter (fun d ->
Printf.printf "SIMPLE MOVING AVERAGE: PERIOD = %d\n" d;
let sma = sma_create d in
List.iter (fun x ->
Printf.printf "Next number = %-2g, SMA = %g\n" x (sma x);
) series;
print_newline ();
) periodLst</lang>
Mathematica
This version uses a list entry so it can use the built-in function. <lang Mathematica>MA[x_List, r_] := Join[Table[Mean[x1;;y],{y,r-1}], MovingAverage[x,r]]</lang>
This version is stateful instead. <lang Mathematica>MAData = {{}, 0}; MAS[x_, t_: Null] :=
With[{r = If[t === Null, MAData2, t]},
Mean[MAData1 =
If[Length[#] > (MAData2 = r), #-r ;; -1, #] &@
Append[MAData1, x]]]</lang>
Tests:
MA[{1, 2, 3, 4, 5, 5, 4, 3, 2, 1}, 5]
=> {1, 3/2, 2, 5/2, 3, 19/5, 21/5, 21/5, 19/5, 3}
MAS[1, 5] => 1
MAS[2] => 3/2
MAS[3] => 2
MAS[4] => 5/2
MAS[5] => 3
MAS[5] => 19/5
MAS[4] => 21/5
MAS[3] => 21/5
MAS[2] => 19/5
MAS[1] => 3
MATLAB / Octave
Matlab and Octave provide very efficient and fast functions, that can be applied to vectors (i.e. series of data samples) <lang Matlab> [m,z] = filter(ones(1,P),P,x); </lang> m is the moving average, z returns the state at the end of the data series, which can be used to continue the moving average. <lang Matlab> [m,z] = filter(ones(1,P),P,x,z); </lang>
Mercury
In Mercury, an idiomatic "moving averages" function would be 'stateless' - or rather, it would have explicit state that its callers would have to thread through uses of it:
<lang Mercury> % state(period, list of floats from [newest, ..., oldest])
- - type state ---> state(int, list(float)).
- - func init(int) = state.
init(Period) = state(Period, []).
- - pred sma(float::in, float::out, state::in, state::out) is det.
sma(N, Average, state(P, L0), state(P, L)) :-
take_upto(P, [N|L0], L),
Average = foldl((+), L, 0.0) / float(length(L)).</lang>
Some notes about this solution: unless P = 0, length(L) can never be 0, as L always incorporates at least N (a step that is accomplished in the arguments to list.take_upto/3). If the implementation of the 'state' type is hidden, and if init/1 checks for P = 0, users of this code can never cause a division-by-zero error in sma/4. Although this solution doesn't try to be as stateful as the task description would like, explicit state is by far simpler and more natural and more straightforward than the alternative in Mercury. Finally, state variables (and higher-order functions that anticipate threaded state) remove much of the potential ugliness or error in threading the same state through many users.
Oz
<lang oz>declare
fun {CreateSMA Period}
Xs = {NewCell nil}
in
fun {$ X}
Xs := {List.take X|@Xs Period}
{FoldL @Xs Number.'+' 0.0}
/
{Int.toFloat {Min Period {Length @Xs}}}
end
end
in
for Period in [3 5] do
SMA = {CreateSMA Period}
in
{System.showInfo "\nSTART PERIOD "#Period}
for I in 1..5 do
{System.showInfo " Number = "#I#" , SMA = "#{SMA {Int.toFloat I}}}
end
for I in 5..1;~1 do
{System.showInfo " Number = "#I#" , SMA = "#{SMA {Int.toFloat I}}}
end
end</lang>
PARI/GP
Partial implementation: does not (yet?) create different stores on each invocation. <lang parigp>sma_per(n)={
sma_v=vector(n); sma_i = 0; n->if(sma_i++>#sma_v,sma_v[sma_i=1]=n;0,sma_v[sma_i]=n;0)+sum(i=1,#sma_v,sma_v[i])/#sma_v
};</lang>
Perl
<lang perl>sub sma ($)
{my ($period, $sum, @a) = shift, 0;
return sub
{unshift @a, shift;
$sum += $a[0];
@a > $period and $sum -= pop @a;
return $sum / @a;}}</lang>
Perl 6
<lang perl6>sub sma (Int $period where (* > 0)) returns Sub {
my $sum = 0;
my @a;
return sub ($x) {
@a.push: $x;
$sum += $x;
$sum -= @a.shift if @a > $period;
return $sum / @a;
}
}</lang>
PL/I
<lang> SMA: procedure (N) returns (float byaddr);
declare N fixed;
declare A(*) fixed controlled,
(p, q) fixed binary static initial (0);
if allocation(A) = 0 then signal error;
p = p + 1; if q < 20 then q = q + 1; if p > hbound(A, 1) then p = 1; A(p) = N; return (sum(float(A))/q);
I: ENTRY (Period);
declare Period fixed binary;
if allocation(A) > 0 then FREE A; allocate A(Period); A = 0; p = 0;
end SMA; </lang>
PicoLisp
<lang PicoLisp>(de sma (@Len)
(curry (@Len (Data)) (N)
(push 'Data N)
(and (nth Data @Len) (con @)) # Truncate
(*/ (apply + Data) (length Data)) ) )</lang>
<lang PicoLisp>(def 'sma3 (sma 3)) (def 'sma5 (sma 5))
(scl 2) (for N (1.0 2.0 3.0 4.0 5.0 5.0 4.0 3.0 2.0 1.0)
(prinl
(format N *Scl)
" (sma3) "
(format (sma3 N) *Scl)
" (sma5) "
(format (sma5 N) *Scl) ) )</lang>
Output:
1.00 (sma3) 1.00 (sma5) 1.00 2.00 (sma3) 1.50 (sma5) 1.50 3.00 (sma3) 2.00 (sma5) 2.00 4.00 (sma3) 3.00 (sma5) 2.50 5.00 (sma3) 4.00 (sma5) 3.00 5.00 (sma3) 4.67 (sma5) 3.80 4.00 (sma3) 4.67 (sma5) 4.20 3.00 (sma3) 4.00 (sma5) 4.20 2.00 (sma3) 3.00 (sma5) 3.80 1.00 (sma3) 2.00 (sma5) 3.00
PureBasic
<lang PureBasic>Procedure.d SMA(Number, Period=0)
Static P Static NewList L() Protected Sum=0 If Period<>0 P=Period EndIf LastElement(L()) AddElement(L()) L()=Number While ListSize(L())>P FirstElement(L()) DeleteElement(L(),1) Wend ForEach L() sum+L() Next ProcedureReturn sum/ListSize(L())
EndProcedure</lang>
Python
Both implementations use the deque datatype.
Procedural
<lang python>from collections import deque
def simplemovingaverage(period):
assert period == int(period) and period > 0, "Period must be an integer >0" summ = n = 0.0 values = deque([0.0] * period) # old value queue
def sma(x):
nonlocal summ, n
values.append(x)
summ += x - values.popleft()
n = min(n+1, period)
return summ / n
return sma</lang>
Class based
<lang python>from collections import deque
class Simplemovingaverage():
def __init__(self, period):
assert period == int(period) and period > 0, "Period must be an integer >0"
self.period = period
self.stream = deque()
def __call__(self, n):
stream = self.stream
stream.append(n) # appends on the right
streamlength = len(stream)
if streamlength > self.period:
stream.popleft()
streamlength -= 1
if streamlength == 0:
average = 0
else:
average = sum( stream ) / streamlength
return average</lang>
Tests <lang python>if __name__ == '__main__':
for period in [3, 5]:
print ("\nSIMPLE MOVING AVERAGE (procedural): PERIOD =", period)
sma = simplemovingaverage(period)
for i in range(1,6):
print (" Next number = %-2g, SMA = %g " % (i, sma(i)))
for i in range(5, 0, -1):
print (" Next number = %-2g, SMA = %g " % (i, sma(i)))
for period in [3, 5]:
print ("\nSIMPLE MOVING AVERAGE (class based): PERIOD =", period)
sma = Simplemovingaverage(period)
for i in range(1,6):
print (" Next number = %-2g, SMA = %g " % (i, sma(i)))
for i in range(5, 0, -1):
print (" Next number = %-2g, SMA = %g " % (i, sma(i)))</lang>
Sample output
SIMPLE MOVING AVERAGE (procedural): PERIOD = 3 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 3 Next number = 5 , SMA = 4 Next number = 5 , SMA = 4.66667 Next number = 4 , SMA = 4.66667 Next number = 3 , SMA = 4 Next number = 2 , SMA = 3 Next number = 1 , SMA = 2 SIMPLE MOVING AVERAGE (procedural): PERIOD = 5 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 2.5 Next number = 5 , SMA = 3 Next number = 5 , SMA = 3.8 Next number = 4 , SMA = 4.2 Next number = 3 , SMA = 4.2 Next number = 2 , SMA = 3.8 Next number = 1 , SMA = 3 SIMPLE MOVING AVERAGE (class based): PERIOD = 3 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 3 Next number = 5 , SMA = 4 Next number = 5 , SMA = 4.66667 Next number = 4 , SMA = 4.66667 Next number = 3 , SMA = 4 Next number = 2 , SMA = 3 Next number = 1 , SMA = 2 SIMPLE MOVING AVERAGE (class based): PERIOD = 5 Next number = 1 , SMA = 1 Next number = 2 , SMA = 1.5 Next number = 3 , SMA = 2 Next number = 4 , SMA = 2.5 Next number = 5 , SMA = 3 Next number = 5 , SMA = 3.8 Next number = 4 , SMA = 4.2 Next number = 3 , SMA = 4.2 Next number = 2 , SMA = 3.8 Next number = 1 , SMA = 3
R
This is easiest done with two functions: one to handle the state (i.e. the numbers already entered), and one to calculate the average. <lang R>#concat concatenates the new values to the existing vector of values, then discards any values that are too old. lastvalues <- local( {
values <- c();
function(x, len)
{
values <<- c(values, x);
lenv <- length(values);
if(lenv > len) values <<- values[(len-lenv):-1]
values
}
})
- moving.average accepts a numeric scalars input (and optionally a length, i.e. the number of values to retain) and calculates the stateful moving average.
moving.average <- function(latestvalue, len=3) {
#Check that all inputs are numeric scalars
is.numeric.scalar <- function(x) is.numeric(x) && length(x)==1L
if(!is.numeric.scalar(latestvalue) || !is.numeric.scalar(len))
{
stop("all arguments must be numeric scalars")
}
#Calculate mean of variables so far
mean(lastvalues(latestvalue, len))
} moving.average(5) # 5 moving.average(1) # 3 moving.average(-3) # 1 moving.average(8) # 2 moving.average(7) # 4</lang>
REXX
The same item list was used as for the ALGOL68 example. <lang rexx> /*REXX program is illustrate simple moving average. */
arg p q n . /*get some arguments (maybe). */ if p== then p=3 /*the 1st period (default: 3).*/ if q== then q=5 /* " 2nd " " 5 */ if n== then n=10 /*number of items in the list.*/ a.=0
do j=1 for n%2 /*build beginning of the list,*/ a.j=j /* ... increasing values. */ end
do k=n%2 to 1 by -1 /* ... decreasing values. */ a.j=k j=j+1 end
do i=1 for n /*show an indented item list. */
say left(,60) 'item' right(i,3)'='right(a.i,3)
end
do i=1 for n /*OK the, let's start the SMA.*/ smaP=sma(p,i) /*simple moving average for P.*/ smaQ=sma(q,i) /* " " " " Q.*/
/*show 2 nicely formated SMAs.*/
say 'i='right(i,3), /*show where we're at in list.*/
" sma("p')='left(sma(p,i),11), /*show nicely aligned sma P. */
" sma("q')='left(sma(q,i),11) /* " " " " Q. */
end
exit
/*────────────────────────────────────────SMA subroutine────────────────*/
sma: procedure expose A.; arg p,j
s=0
i=0
do k=max(1,j-p+1) to j+p for p while k<=j i=i+1 s=s+a.k end
return s/i </lang> Output when the defaults were used:
item 1= 1
item 2= 2
item 3= 3
item 4= 4
item 5= 5
item 6= 5
item 7= 4
item 8= 3
item 9= 2
item 10= 1
i= 1 sma(3)=1 sma(5)=1
i= 2 sma(3)=1.5 sma(5)=1.5
i= 3 sma(3)=2 sma(5)=2
i= 4 sma(3)=3 sma(5)=2.5
i= 5 sma(3)=4 sma(5)=3
i= 6 sma(3)=4.66666667 sma(5)=3.8
i= 7 sma(3)=4.66666667 sma(5)=4.2
i= 8 sma(3)=4 sma(5)=4.2
i= 9 sma(3)=3 sma(5)=3.8
i= 10 sma(3)=2 sma(5)=3
Ruby
A closure: <lang ruby>def simple_moving_average(size)
nums = [] sum = 0.0 lambda do |hello| nums << hello goodbye = nums.length > size ? nums.shift : 0 sum += hello - goodbye sum / nums.length end
end
ma3 = simple_moving_average(3) ma5 = simple_moving_average(5)
(1.upto(5).to_a + 5.downto(1).to_a).each do |num|
printf "Next number = %d, SMA_3 = %.3f, SMA_5 = %.1f\n", num, ma3.call(num), ma5.call(num)
end</lang>
A class <lang ruby>class MovingAverager
def initialize(size) @size = size @nums = [] @sum = 0.0 end def <<(hello) @nums << hello goodbye = @nums.length > @size ? @nums.shift : 0 @sum += hello - goodbye self end def average @sum / @nums.length end alias to_f average def to_s average.to_s end
end
ma3 = MovingAverager.new(3) ma5 = MovingAverager.new(5)
(1.upto(5).to_a + 5.downto(1).to_a).each do |num|
printf "Next number = %d, SMA_3 = %.3f, SMA_5 = %.1f\n", num, ma3 << num, ma5 <<num
end</lang>
Scala
<lang scala>class MovingAverage(period: Int) {
private var queue = new scala.collection.mutable.Queue[Double]()
def apply(n: Double) = {
queue.enqueue(n)
if (queue.size > period)
queue.dequeue
queue.sum / queue.size
}
override def toString = queue.mkString("(", ", ", ")")+", period "+period+", average "+(queue.sum / queue.size)
def clear = queue.clear
}</lang>
scala> List(3,5) foreach { period =>
| println("SIMPLE MOVING AVERAGE: PERIOD = "+period)
| val sma = new MovingAverage(period)
| 1.0 to 5.0 by 1.0 foreach {i => println(" Next number = %-2g, SMA = %g " format (i, sma(i)))}
| 5.0 to 1.0 by -1.0 foreach {i => println(" Next number = %-2g, SMA = %g " format (i, sma(i)))}
| println(sma+"\n")
| }
SIMPLE MOVING AVERAGE: PERIOD = 3
Next number = 1.00000, SMA = 1.00000
Next number = 2.00000, SMA = 1.50000
Next number = 3.00000, SMA = 2.00000
Next number = 4.00000, SMA = 3.00000
Next number = 5.00000, SMA = 4.00000
Next number = 5.00000, SMA = 4.66667
Next number = 4.00000, SMA = 4.66667
Next number = 3.00000, SMA = 4.00000
Next number = 2.00000, SMA = 3.00000
Next number = 1.00000, SMA = 2.00000
(3.0, 2.0, 1.0), period 3, average 2.0
SIMPLE MOVING AVERAGE: PERIOD = 5
Next number = 1.00000, SMA = 1.00000
Next number = 2.00000, SMA = 1.50000
Next number = 3.00000, SMA = 2.00000
Next number = 4.00000, SMA = 2.50000
Next number = 5.00000, SMA = 3.00000
Next number = 5.00000, SMA = 3.80000
Next number = 4.00000, SMA = 4.20000
Next number = 3.00000, SMA = 4.20000
Next number = 2.00000, SMA = 3.80000
Next number = 1.00000, SMA = 3.00000
(5.0, 4.0, 3.0, 2.0, 1.0), period 5, average 3.0
Scheme
<lang scheme>(define ((simple-moving-averager size . nums) num)
(set! nums (cons num (if (= (length nums) size) (reverse (cdr (reverse nums))) nums))) (/ (apply + nums) (length nums)))
(define av (simple-moving-averager 3)) (map av '(1 2 3 4 5 5 4 3 2 1)) </lang> Output:
(1 3/2 2 3 4 14/3 14/3 4 3 2)
Smalltalk
<lang smalltalk>Object subclass: MovingAverage [
|valueCollection period collectedNumber sum| MovingAverage class >> newWithPeriod: thePeriod [
|r| r := super basicNew. ^ r initWithPeriod: thePeriod
] initWithPeriod: thePeriod [ valueCollection := OrderedCollection new: thePeriod.
period := thePeriod. collectedNumber := 0. sum := 0
]
sma [ collectedNumber < period
ifTrue: [ ^ sum / collectedNumber ]
ifFalse: [ ^ sum / period ] ]
add: value [
collectedNumber < period
ifTrue: [
sum := sum + value. valueCollection add: value. collectedNumber := collectedNumber + 1. ] ifFalse: [ sum := sum - (valueCollection removeFirst). sum := sum + value. valueCollection add: value ]. ^ self sma
]
].</lang>
<lang smalltalk>|sma3 sma5|
sma3 := MovingAverage newWithPeriod: 3. sma5 := MovingAverage newWithPeriod: 5.
- ( 1 2 3 4 5 5 4 3 2 1 ) do: [ :v |
('Next number %1, SMA_3 = %2, SMA_5 = %3' % {
v . (sma3 add: v) asFloat . (sma5 add: v) asFloat
}) displayNl
]</lang>
Tcl
or
<lang tcl>oo::class create SimpleMovingAverage {
variable vals idx constructor Template:Period 3 { set idx end-[expr {$period-1}] set vals {} } method val x { set vals [lrange [list {*}$vals $x] $idx end] expr {[tcl::mathop::+ {*}$vals]/double([llength $vals])} }
}</lang> Demonstration: <lang tcl>SimpleMovingAverage create averager3 SimpleMovingAverage create averager5 5 foreach n {1 2 3 4 5 5 4 3 2 1} {
puts "Next number = $n, SMA_3 = [averager3 val $n], SMA_5 = [averager5 val $n]"
}</lang> Output:
Next number = 1, SMA_3 = 1.0, SMA_5 = 1.0 Next number = 2, SMA_3 = 1.5, SMA_5 = 1.5 Next number = 3, SMA_3 = 2.0, SMA_5 = 2.0 Next number = 4, SMA_3 = 3.0, SMA_5 = 2.5 Next number = 5, SMA_3 = 4.0, SMA_5 = 3.0 Next number = 5, SMA_3 = 4.666666666666667, SMA_5 = 3.8 Next number = 4, SMA_3 = 4.666666666666667, SMA_5 = 4.2 Next number = 3, SMA_3 = 4.0, SMA_5 = 4.2 Next number = 2, SMA_3 = 3.0, SMA_5 = 3.8 Next number = 1, SMA_3 = 2.0, SMA_5 = 3.0
TI-83 BASIC
Continuously prompts for an input I, which is added to the end of a list L1. L1 can be found by pressing "2ND"/"1", and mean can be found in "List"/"OPS"
Press ON to terminate the program.
<lang ti83b>:1->C
- While 1
- Prompt I
- C->dim(L1)
- I->L1(C)
- Disp mean(L1)
- 1+C->C
- End</lang>
TI-89 BASIC
Function that returns a list containing the averaged data of the supplied argument <lang ti89b>movinavg(list,p) Func
Local r, i, z For i,1,dim(list) max(i-p,0)→z sum(mid(list,z+1,i-z))/(i-z)→r[i] EndFor r
EndFunc
</lang>
Program that returns a simple value at each invocation: <lang ti89b>movinav2(x_,v_) Prgm
If getType(x_)="STR" Then
{}→list
v_→p
Return
EndIf
right(augment(list,{x_}),p)→list
sum(list)/dim(list)→#v_
EndPrgm </lang>
Example1: Using the function
movinavg({1,2,3,4,5,6,7,8,9,10},5)
list is the list being averaged: {1,2,3,4,5,6,7,8,9,10}
p is the period: 5
returns the averaged list: {1, 3/2, 2, 5/2, 3, 4, 5, 6, 7, 8}
Example 2: Using the program
movinav2("i",5) - Initializing moving average calculation, and define period of 5
movinav2(3, "x"):x - new data in the list (value 3), and result will be stored on variable x, and displayed
movinav2(4, "x"):x - new data (value 4), and the new result will be stored on variable x, and displayed (4+3)/2
...
Description of the function movinavg:
variable r - is the result (the averaged list) that will be returned
variable i - is the index variable, and it points to the end of the sub-list the list being averaged.
variable z - an helper variable
The function uses variable i to determine which values of the list will be considered in the next average calculation.
At every iteration, variable i points to the last value in the list that will be used in the average calculation.
So we only need to figure out which will be the first value in the list.
Usually we'll have to consider p elements, so the first element will be the one indexed by (i-p+1).
However on the first iterations that calculation will usually be negative, so the following equation will avoid negative indexes: max(i-p+1,1) or, arranging the equation, max(i-p,0)+1.
But the number of elements on the first iterations will also be smaller, the correct value will be (end index - begin index + 1) or, arranging the equation, (i - (max(i-p,0)+1) +1) ,and then, (i-max(i-p,0)).
Variable z holds the common value (max(i-p),0) so the begin_index will be (z+1) and the number_of_elements will be (i-z)
mid(list,z+1, i-z) will return the list of value that will be averaged
sum(...) will sum them
sum(...)/(i-z) → r[i] will average them and store the result in the appropriate place in the result list
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