Averages/Simple moving average: Difference between revisions

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=={{header|C}}==
=={{header|C}}==
The code in the first section duplicates the code for the Standard Deviation Task.
<lang c>#include <stdio.h>
<lang c>#include <stdio.h>
#include <stdlib.h>
#include <stdlib.h>
#include <math.h>
#include <stdarg.h>

typedef struct sma_obj {
enum Action { STDDEV, MEAN, VAR, COUNT };
double sma;
double sum;
typedef struct stat_obj_struct {
int period;
double sum, sum2;
double *values;
size_t num;
int lv;
Action action;
} sma_obj_t;
} sStatObject, *StatObject;

typedef union sma_result {
StatObject NewStatObject( Action action )
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;
so = (StatObject)malloc(sizeof(sStatObject));
sma_result_t r;
so->sum = 0.0;
so->sum2 = 0.0;
sma_obj_t *o;
so->num = 0;
double v;

so->action = action;
va_start(vl, action);
return so;
}
#define FREE_STAT_OBJECT(so) \
free(so); so = NULL
double stat_obj_value(StatObject so, Action action)
{
double m;
if (so->num == 0.0) return 0.0;
switch(action) {
switch(action) {
case STDDEV:
case SMA_NEW: // args: int period
r.handle = malloc(sizeof(sma_obj_t));
m = so->sum/so->num;
return sqrt(so->sum2/so->num - m*m);
r.handle->sma = 0.0;
r.handle->period = va_arg(vl, int);
case MEAN:
r.handle->values = malloc(r.handle->period * sizeof(double));
return so->sum/so->num;
r.handle->lv = 0;
case VAR:
m = so->sum/so->num;
r.handle->sum = 0.0;
break;
return so->sum2/so->num - m*m;
case SMA_FREE: // args: sma_obj_t *handle
case COUNT:
r.handle = va_arg(vl, sma_obj_t *);
return 1.0*so->num;
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;
double stat_object_add(StatObject so, double v)
{
so->num++;
so->sum += v;
so->sum2 += v*v;
return stat_obj_value(so->action);
}</lang>
}</lang>

The following code creates the StatObject so that the add returns the running average.
<lang c>double v[] = { 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 };
<lang c>double v[] = { 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 };

int main()
int main()
{
{
int i;
int i;

StatObject so = NewStatObject( MEAN );
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("val: %lf mean: %lf\n", v[i], stat_object_add(so, v[i]));
for(i=0; i < sizeof(v)/sizeof(double) ; i++) {
printf("next number %lf, SMA_3 = %lf, SMA_5 = %lf\n",
FREE_STAT_OBJECT(so);
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;
return 0;
}</lang>
}</lang>

Revision as of 17:19, 16 January 2010

Task
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.

Create a stateful function/class/instance that takes a number as argument and returns a simple moving average of its arguments so far.

Note that the moving average has a period and numbers beyond the period must be dropped from the calculation of the average. (See the Python example, amongst others, for a correct implementation) .

See also: Standard Deviation

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>

ALGOL 68

Translation of: C
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

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

C

<lang c>#include <stdio.h>

  1. include <stdlib.h>
  2. 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>

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

This should work properly for any types that act like numerics. <lang d>import std.stdio; import std.string;

class MovingAvg(T) { 

       T[]elements;
       int window = 5;
       MovingAvg!(T) add(T input) {
               elements ~= input;
               return this;
       }
       void setWindow(int win) {window = win;}
       T getAvg() {
               if (!window) return 0;
               T sum = 0;
               int start = (elements.length-window<0?elements.length:elements.length-window);
               if (start == elements.length) return 0;
               foreach(ele;elements[start..$]) {sum += ele;}
               return sum/(elements.length-start);
       }

}

int main() { 

       double[]nums = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1];
       auto mavg = new MovingAvg!(double);
       foreach(index,num;nums) {
               writefln("Average number %d is %s",index,toString(mavg.add(num).getAvg));
       }
       return 0;

}</lang>

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>

<lang e>? for period in [3, 5] {

> 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>

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

Works with: Fortran version 90 and later

<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>

Groovy

Translation of: Ruby

<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

Works with: GHC version 6.10.4

<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

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 (+/%#)\.

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.

Java

Works with: Java version 1.5+

<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

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: <lang Mathematica> 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 </lang>

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>

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

Works with: Rakudo version #22 "Thousand Oaks"

<lang perl6>sub sma (Int $period where (* > 0)) returns Sub { 

 my ($sum, @a) = 0;
 return sub ($x) {
     unshift @a, $x;
     $sum += $x;
     @a > $period and $sum -= pop @a;
     return $sum / @a;
 }

}</lang>

Python

Works with: Python version 3.x

<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


if __name__ == '__main__': 

   for period in [3, 5]:
       print ("\nSIMPLE MOVING AVERAGE: 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: 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

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
  }

})

  1. 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>

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

Works with: GNU 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. ( 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

Works with: Tcl version 8.6

<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

This example is incorrect. Please fix the code and remove this message.

Details: It is not stateful: it does not return any averages before all of the data is provided.

Prompts for a source list A and the length K of the moving average. The 'L' in "LB" and "LB" is found in "List"/"OPS". <lang ti83b>:Prompt LA,K

For(I,1,dim(LA))
0→S
For(J,I-K+1,I)
If J≥1
S+LA(J)→S
End
S/K→LB(I)
End</lang>

TI-89 BASIC

This example is incorrect. Please fix the code and remove this message.

Details: It is not stateful: it does not return any averages before all of the data is provided.

<lang ti89b>movinavg(la,k) Func 

 Local lb,s,i,j
 For i,1,dim(la)
   0→s
   For j,i-k+1,i
     If j≥1 Then
       s+la[j]→s
     EndIf
   EndFor
   s/k→lb[i]
 EndFor
 Return lb</lang>
EndFunc
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