Averages/Simple moving average
(Redirected from Average/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.
- Task
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.
Pseudo-code 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
| ||||||||||||||||||||||||||||||||||||||||||||||
11l
T SMA
[Float] data
sum = 0.0
index = 0
n_filled = 0
Int period
F (period)
.period = period
.data = [0.0] * period
F add(v)
.sum += v - .data[.index]
.data[.index] = v
.index = (.index + 1) % .period
.n_filled = min(.period, .n_filled + 1)
R .sum / .n_filled
V sma3 = SMA(3)
V sma5 = SMA(5)
L(e) [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]
print(‘Added #., sma(3) = #.6, sma(5) = #.6’.format(e, sma3.add(e), sma5.add(e)))- 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
360 Assembly
* Averages/Simple moving average 26/08/2015
AVGSMA CSECT
USING AVGSMA,R12
LR R12,R15
ST R14,SAVER14
ZAP II,=P'0' ii=0
LA R7,1
LH R3,NA
SRA R3,1 na/2
LOOPA CR R7,R3 do i=1 to na/2
BH ELOOPA
AP II,=P'1000' ii=ii+1000
LR R1,R7 i
MH R1,=H'6'
LA R4,A-6(R1)
MVC 0(6,R4),II a(i)=ii
LH R1,NA na
SR R1,R7 -i
MH R1,=H'6'
LA R4,A(R1)
MVC 0(6,R4),II a(na+1-i)=ii
LA R7,1(R7)
B LOOPA
ELOOPA XPRNT =CL30' n sma3 sma5 ',30
XPRNT =CL30' ----- ----------- -----------',30
LA R7,1 i=1
LOOP CH R7,NA do i=1 to na
BH RETURN
STH R7,N n=i
XDECO R7,C i
MVC BUF+1(5),C+7
MVC P,=H'3' p=3
BAL R14,SMA
MVC C(13),EDMASK
ED C(13),SS sma(3,i)
MVC BUF+7(11),C+2
MVC P,=H'5' p=5
BAL R14,SMA
MVC C(13),EDMASK
ED C(13),SS sma(5,i)
MVC BUF+19(11),C+2
XPRNT BUF,30 output i,sma3,sma5
LA R7,1(R7)
B LOOP
* ***** sub sma(p,n) returns(PL6)
SMA LH R5,N
SH R5,P
A R5,=F'1' ia=n-p+1
C R5,=F'1'
BH OKIA
LA R5,1 ia=1
OKIA LH R6,NA ib=na
CH R6,N
BL OKIB
LH R6,N ib=n
OKIB ZAP II,=P'0' ii=0
ZAP SS,=P'0' ss=0
LR R3,R5 k=ia
LOOPK CR R3,R6 do k=ia to ib
BH ELOOPK
AP II,=P'1' ii=ii+1
LR R1,R3
MH R1,=H'6'
LA R4,A-6(R1)
MVC C(6),0(R4) ss=ss+a(k)
AP SS,C(6)
LA R3,1(R3)
B LOOPK
ELOOPK ZAP C,SS
DP C,II
ZAP SS,C(10) ss=ss/ii
BR R14
RETURN L R14,SAVER14 restore caller address
XR R15,R15
BR R14
SAVER14 DS F
NN EQU 10
NA DC AL2(NN)
A DS (NN)PL6
II DS PL6
SS DS PL6
P DS H
N DS H
C DS CL16
BUF DC CL30' ' buffer
EDMASK DC X'4020202020202021204B202020' CL13
YREGS
END AVGSMA- Output:
n sma3 sma5
----- ----------- -----------
1 1.000 1.000
2 1.500 1.500
3 2.000 2.000
4 3.000 2.500
5 4.000 3.000
6 4.666 3.800
7 4.666 4.200
8 4.000 4.200
9 3.000 3.800
10 2.000 3.000
Ada
moving.ads:
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;
moving.adb:
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;
main.adb:
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;
- 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.
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))
#
)- 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:
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
}
For floating point numbers:
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
}
AWK
#!/usr/bin/awk -f
# Moving average over the first column of a data file
BEGIN {
P = 5;
}
{
x = $1;
i = NR % P;
MA += (x - Z[i]) / P;
Z[i] = x;
print MA;
}
BBC BASIC
MAXPERIOD = 10
FOR n = 1 TO 5
PRINT "Number = ";n TAB(12) " SMA3 = ";FNsma(n,3) TAB(30) " SMA5 = ";FNsma(n,5)
NEXT
FOR n = 5 TO 1 STEP -1
PRINT "Number = ";n TAB(12) " SMA3 = ";FNsma(n,3) TAB(30) " SMA5 = ";FNsma(n,5)
NEXT
END
DEF FNsma(number, period%)
PRIVATE nums(), accum(), index%(), window%()
DIM nums(MAXPERIOD,MAXPERIOD), accum(MAXPERIOD)
DIM index%(MAXPERIOD), window%(MAXPERIOD)
accum(period%) += number - nums(period%,index%(period%))
nums(period%,index%(period%)) = number
index%(period%) = (index%(period%) + 1) MOD period%
IF window%(period%)<period% window%(period%) += 1
= accum(period%) / window%(period%)
- Output:
Number = 1 SMA3 = 1 SMA5 = 1 Number = 2 SMA3 = 1.5 SMA5 = 1.5 Number = 3 SMA3 = 2 SMA5 = 2 Number = 4 SMA3 = 3 SMA5 = 2.5 Number = 5 SMA3 = 4 SMA5 = 3 Number = 5 SMA3 = 4.66666667 SMA5 = 3.8 Number = 4 SMA3 = 4.66666667 SMA5 = 4.2 Number = 3 SMA3 = 4 SMA5 = 4.2 Number = 2 SMA3 = 3 SMA5 = 3.8 Number = 1 SMA3 = 2 SMA5 = 3
BQN
SMA takes moving average of a list, given the whole array.
SMA2 returns a stateful function which can be run on individual numbers of a stream.
SMA ← {(+´÷≠)¨(1↓𝕨↑↑𝕩)∾<˘𝕨↕𝕩}
v ← (⊢∾⌽)1+↕5
•Show 5 SMA v
SMA2 ← {
𝕊 size:
nums ← ⟨⟩
sum ← 0
{
nums ∾↩ 𝕩
gb ← {(≠nums)≤size ? 0 ; a←⊑nums, nums↩1↓nums, a}
sum +↩ 𝕩 - gb
sum ÷ ≠nums
}
}
fun ← SMA2 5
Fun¨ v
⟨ 1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3 ⟩ ⟨ 1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3 ⟩
Bracmat
( ( I
= buffer
. (new$=):?freshEmptyBuffer
&
' ( buffer avg
. ( avg
= L S n
. 0:?L:?S
& whl
' ( !arg:%?n ?arg
& !n+!S:?S
& 1+!L:?L
)
& (!L:0&0|!S*!L^-1)
)
& (buffer=$freshEmptyBuffer)
& !arg !(buffer.):?(buffer.)
& ( !(buffer.):?(buffer.) [($arg) ?
|
)
& avg$!(buffer.)
)
)
& ( pad
= len w
. @(!arg:? [?len)
& @(" ":? [!len ?w)
& !w !arg
)
& I$3:(=?sma3)
& I$5:(=?sma5)
& 1 2 3 4 5 5 4 3 2 1:?K
& whl
' ( !K:%?k ?K
& out
$ (str$(!k " - sma3:" pad$(sma3$!k) " sma5:" pad$(sma5$!k)))
)
);- Output:
1 - sma3: 1 sma5: 1 2 - sma3: 3/2 sma5: 3/2 3 - sma3: 2 sma5: 2 4 - sma3: 3 sma5: 5/2 5 - sma3: 4 sma5: 3 5 - sma3: 14/3 sma5: 19/5 4 - sma3: 14/3 sma5: 21/5 3 - sma3: 4 sma5: 21/5 2 - sma3: 3 sma5: 19/5 1 - sma3: 2 sma5: 3
Brat
Object version
SMA = object.new
SMA.init = { period |
my.period = period
my.list = []
my.average = 0
}
SMA.prototype.add = { num |
true? my.list.length >= my.period
{ my.list.deq }
my.list << num
my.average = my.list.reduce(:+) / my.list.length
}
sma3 = SMA.new 3
sma5 = SMA.new 5
[1, 2, 3, 4, 5, 5, 4, 3, 2, 1].each { n |
p n, " - SMA3: ", sma3.add(n), " SMA5: ", sma5.add(n)
}Function version
sma = { period |
list = []
{ num |
true? list.length >= period
{ list.deq }
list << num
list.reduce(:+) / list.length
}
}
sma3 = sma 3
sma5 = sma 5
[1, 2, 3, 4, 5, 5, 4, 3, 2, 1].each { n |
p n, " - SMA3: ", sma3(n), " SMA5: ", sma5(n)
}- 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: 4.6666666666667 SMA5: 3.8 4 - SMA3: 4.6666666666667 SMA5: 4.2 3 - SMA3: 4 SMA5: 4.2 2 - SMA3: 3 SMA5: 3.8 1 - SMA3: 2 SMA5: 3
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;
}
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;
}
C#
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();
};
}
}
}
- 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
C++
#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;
}
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.
(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)))))
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)
- Output:
> 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
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.
(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))))
Use
(mapcar '(simple-moving-average period) list-of-values)
Crystal
def sma(n) Proc(Float64, Float64)
a = Array(Float64).new
->(x : Float64) {
a.shift if a.size == n
a.push x
a.sum / a.size.to_f
}
end
sma3, sma5 = sma(3), sma(5)
# Copied from the Ruby solution.
(1.upto(5).to_a + 5.downto(1).to_a).each do |n|
printf "%d: sma3 = %.3f - sma5 = %.3f\n", n, sma3.call(n.to_f), sma5.call(n.to_f)
end
1: sma3 = 1.000 - sma5 = 1.000 2: sma3 = 1.500 - sma5 = 1.500 3: sma3 = 2.000 - sma5 = 2.000 4: sma3 = 3.000 - sma5 = 2.500 5: sma3 = 4.000 - sma5 = 3.000 5: sma3 = 4.667 - sma5 = 3.800 4: sma3 = 4.667 - sma5 = 4.200 3: sma3 = 4.000 - sma5 = 4.200 2: sma3 = 3.000 - sma5 = 3.800 1: sma3 = 2.000 - sma5 = 3.000
D
Using a Closure
Currently this sma can't be @nogc because it allocates a closure on the heap. Some escape analysis could remove the heap allocation.
import std.stdio, std.traits, std.algorithm;
auto sma(T, int period)() pure nothrow @safe {
T[period] data = 0;
T sum = 0;
int index, nFilled;
return (in T v) nothrow @safe @nogc {
sum += -data[index] + v;
data[index] = v;
index = (index + 1) % period;
nFilled = min(period, nFilled + 1);
return CommonType!(T, float)(sum) / nFilled;
};
}
void main() {
immutable s3 = sma!(int, 3);
immutable s5 = sma!(double, 5);
foreach (immutable 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));
}
- 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 keeping the data in the stack frame of the main function. Same output:
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 @safe @nogc {
sum += -data[index] + v;
data[index] = v;
index = (index + 1) % period;
nFilled = min(period, nFilled + 1);
return CommonType!(T, float)(sum) / nFilled;
}
}
void main() {
SMA!(int, 3) s3;
SMA!(double, 5) s5;
foreach (immutable 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));
}
To avoid the floating point approximations keep piling up and growing, the code could perform a periodic sum on the whole circular queue array.
Delphi
Small variation of #Pascal.
program Simple_moving_average;
{$APPTYPE CONSOLE}
type
TMovingAverage = record
private
buffer: TArray<Double>;
head: Integer;
Capacity: Integer;
Count: Integer;
sum, fValue: Double;
public
constructor Create(aCapacity: Integer);
function Add(Value: Double): Double;
procedure Reset;
property Value: Double read fValue;
end;
{ TMovingAverage }
function TMovingAverage.Add(Value: Double): Double;
begin
head := (head + 1) mod Capacity;
sum := sum + Value - buffer[head];
buffer[head] := Value;
if count < capacity then
begin
inc(Count);
fValue := sum / count;
exit(fValue);
end;
fValue := sum / Capacity;
Result := fValue;
end;
constructor TMovingAverage.Create(aCapacity: Integer);
begin
Capacity := aCapacity;
SetLength(buffer, aCapacity);
Reset;
end;
procedure TMovingAverage.Reset;
var
i: integer;
begin
head := -1;
Count := 0;
sum := 0;
fValue := 0;
for i := 0 to High(buffer) do
buffer[i] := 0;
end;
var
avg3, avg5: TMovingAverage;
i: Integer;
begin
avg3 := TMovingAverage.Create(3);
avg5 := TMovingAverage.Create(5);
for i := 1 to 5 do
begin
write('Inserting ', i, ' into avg3 ', avg3.Add(i): 0: 4);
writeln(' Inserting ', i, ' into avg5 ', avg5.Add(i): 0: 4);
end;
for i := 5 downto 1 do
begin
write('Inserting ', i, ' into avg3 ', avg3.Add(i): 0: 4);
writeln(' Inserting ', i, ' into avg5 ', avg5.Add(i): 0: 4);
end;
avg3.Reset;
for i := 1 to 100000000 do
avg3.Add(i);
writeln('100''000''000 insertions ', avg3.Value: 0: 4);
Readln;
end.
- Output:
Inserting 1 into avg3 1.0000 Inserting 1 into avg5 1.0000 Inserting 2 into avg3 1.5000 Inserting 2 into avg5 1.5000 Inserting 3 into avg3 2.0000 Inserting 3 into avg5 2.0000 Inserting 4 into avg3 3.0000 Inserting 4 into avg5 2.5000 Inserting 5 into avg3 4.0000 Inserting 5 into avg5 3.0000 Inserting 5 into avg3 4.6667 Inserting 5 into avg5 3.8000 Inserting 4 into avg3 4.6667 Inserting 4 into avg5 4.2000 Inserting 3 into avg3 4.0000 Inserting 3 into avg5 4.2000 Inserting 2 into avg3 3.0000 Inserting 2 into avg5 3.8000 Inserting 1 into avg3 2.0000 Inserting 1 into avg5 3.0000 100'000'000 insertions 99999999.0000
Dyalect
func avg(xs) {
var acc = 0.0
var c = 0
for x in xs {
c += 1
acc += x
}
acc / c
}
func sma(p) {
var s = []
x => {
if s.Length() >= p {
s.RemoveAt(0)
}
s.Insert(s.Length(), x)
avg(s)
};
}
var nums = Iterator.Concat(1.0..5.0, 5.0^-1.0..1.0)
var sma3 = sma(3)
var sma5 = sma(5)
for n in nums {
print("\(n)\t(sma3) \(sma3(n))\t(sma5) \(sma5(n))")
}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.
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]
}? 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 3.0EasyLang
prefix sma_
global p[] ind[] sum[] smpl[][] .
func new p .
p[] &= p
ind[] &= 0
sum[] &= 0
smpl[][] &= [ ]
return len p[]
.
func get id x .
ind[id] = (ind[id] + 1) mod1 p[id]
ind = ind[id]
if len smpl[id][] < ind
len smpl[id][] ind
else
sum[id] -= smpl[id][ind]
.
sum[id] += x
smpl[id][ind] = x
return sum[id] / len smpl[id][]
.
prefix
#
sma5 = sma_new 5
sma3 = sma_new 3
numfmt 2 4
for v in [ 1 2 3 4 5 5 4 3 2 1 ]
print sma_get sma3 v & " " & sma_get sma5 v
.
EchoLisp
(lib 'tree) ;; queues operations
(define (make-sma p)
(define Q (queue (gensym)))
(lambda (item)
(q-push Q item)
(when (> (queue-length Q) p) (q-pop Q))
(// (for/sum ((x (queue->list Q))) x) (queue-length Q))))
- Output:
(define serie '(1 2 3 4 5 5 4 3 2 1)) (define sma-3 (make-sma 3)) (define sma-5 (make-sma 5)) (for ((x serie)) (printf "%3d %10d %10d" x (sma-3 x) (sma-5 x))) 1 1 1 2 1.5 1.5 3 2 2 4 3 2.5 5 4 3 5 4.6667 3.8 4 4.6667 4.2 3 4 4.2 2 3 3.8 1 2 3
Elena
ELENA 6.x :
import system'routines;
import system'collections;
import extensions;
class SMA
{
object thePeriod;
object theList;
constructor new(period)
{
thePeriod := period;
theList :=new List();
}
append(n)
{
theList.append(n);
var count := theList.Length;
count =>
0 { ^0.0r }
! {
if (count > thePeriod)
{
theList.removeAt(0);
count := thePeriod
};
var sum := theList.summarize(Real.new());
^ sum / count
}
}
}
// --- Program ---
public program()
{
var SMA3 := SMA.new(3);
var SMA5 := SMA.new(5);
for (int i := 1; i <= 5; i += 1) {
console.printPaddingRight(30, "sma3 + ", i, " = ", SMA3.append(i));
console.printLine("sma5 + ", i, " = ", SMA5.append(i))
};
for (int i := 5; i >= 1; i -= 1) {
console.printPaddingRight(30, "sma3 + ", i, " = ", SMA3.append(i));
console.printLine("sma5 + ", i, " = ", SMA5.append(i))
};
console.readChar()
}- Output:
sma3 + 1 = 1.0 sma5 + 1 = 1.0 sma3 + 2 = 1.5 sma5 + 2 = 1.5 sma3 + 3 = 2.0 sma5 + 3 = 2.0 sma3 + 4 = 3.0 sma5 + 4 = 2.5 sma3 + 5 = 4.0 sma5 + 5 = 3.0 sma3 + 5 = 4.666666666667 sma5 + 5 = 3.8 sma3 + 4 = 4.666666666667 sma5 + 4 = 4.2 sma3 + 3 = 4.0 sma5 + 3 = 4.2 sma3 + 2 = 3.0 sma5 + 2 = 3.8 sma3 + 1 = 2.0 sma5 + 1 = 3.0
Elixir
The elixir program below generates an anonymous function with an embedded period `p`, which is used as the period of the simple moving average. The `run` function reads numeric input and passes it to the newly created anonymous function, and then "inspects" the result to STDOUT.
$ cat simple-moving-avg.exs
#!/usr/bin/env elixir
defmodule Math do
def average([]), do: nil
def average(enum) do
Enum.sum(enum) / length(enum)
end
end
defmodule SMA do
def sma(l, p \\ 10) do
IO.puts("\nSimple moving average(period=#{p}):")
Enum.chunk(l, p, 1)
|> Enum.map(&(%{"input": &1, "avg": Float.round(Math.average(&1), 3)}))
end
defmacro gen_func(p) do
quote do
fn l -> SMA.sma(l, unquote(p)) end
end
end
def read_numeric_input do
IO.stream(:stdio, :line)
|> Enum.map(&(String.split(&1, ~r{\s+})))
|> List.flatten()
|> Enum.reject(&(is_nil(&1) || String.length(&1) == 0))
|> Enum.map(&(Integer.parse(&1) |> elem(0)))
end
def run do
sma_func_10 = gen_func(10)
sma_func_15 = gen_func(15)
numbers = read_numeric_input
sma_func_10.(numbers) |> IO.inspect
sma_func_15.(numbers) |> IO.inspect
end
end
SMA.run
#!/bin/bash
elixir ./simple-moving-avg.exs <<EOF
1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1
2 4 6 8 10 12 14 12 10 8 6 4 2
EOF
The output is shown below, with the average, followed by the grouped input, forming the basis of each moving average.
$ ./simple-moving-avg.sh
Simple moving average(period=10):
[%{avg: 5.3, input: [1, 2, 3, 4, 5, 6, 7, 8, 9, 8]},
%{avg: 5.9, input: [2, 3, 4, 5, 6, 7, 8, 9, 8, 7]},
%{avg: 6.3, input: [3, 4, 5, 6, 7, 8, 9, 8, 7, 6]},
%{avg: 6.5, input: [4, 5, 6, 7, 8, 9, 8, 7, 6, 5]},
%{avg: 6.5, input: [5, 6, 7, 8, 9, 8, 7, 6, 5, 4]},
%{avg: 6.3, input: [6, 7, 8, 9, 8, 7, 6, 5, 4, 3]},
%{avg: 5.9, input: [7, 8, 9, 8, 7, 6, 5, 4, 3, 2]},
%{avg: 5.3, input: [8, 9, 8, 7, 6, 5, 4, 3, 2, 1]},
%{avg: 4.7, input: [9, 8, 7, 6, 5, 4, 3, 2, 1, 2]},
%{avg: 4.2, input: [8, 7, 6, 5, 4, 3, 2, 1, 2, 4]},
%{avg: 4.0, input: [7, 6, 5, 4, 3, 2, 1, 2, 4, 6]},
%{avg: 4.1, input: [6, 5, 4, 3, 2, 1, 2, 4, 6, 8]},
%{avg: 4.5, input: [5, 4, 3, 2, 1, 2, 4, 6, 8, 10]},
%{avg: 5.2, input: [4, 3, 2, 1, 2, 4, 6, 8, 10, 12]},
%{avg: 6.2, input: [3, 2, 1, 2, 4, 6, 8, 10, 12, 14]},
%{avg: 7.1, input: [2, 1, 2, 4, 6, 8, 10, 12, 14, 12]},
%{avg: 7.9, input: [1, 2, 4, 6, 8, 10, 12, 14, 12, 10]},
%{avg: 8.6, input: [2, 4, 6, 8, 10, 12, 14, 12, 10, 8]},
%{avg: 9.0, input: [4, 6, 8, 10, 12, 14, 12, 10, 8, 6]},
%{avg: 9.0, input: [6, 8, 10, 12, 14, 12, 10, 8, 6, 4]},
%{avg: 8.6, input: [8, 10, 12, 14, 12, 10, 8, 6, 4, 2]}]
Simple moving average(period=15):
[%{avg: 5.2, input: [1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3]},
%{avg: 5.267, input: [2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2]},
%{avg: 5.2, input: [3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]},
%{avg: 5.133, input: [4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2]},
%{avg: 5.133, input: [5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 4]},
%{avg: 5.2, input: [6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 4, 6]},
%{avg: 5.333, input: [7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 4, 6, 8]},
%{avg: 5.533, input: [8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 4, 6, 8, 10]},
%{avg: 5.8, input: [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 4, 6, 8, 10, 12]},
%{avg: 6.133, input: [8, 7, 6, 5, 4, 3, 2, 1, 2, 4, 6, 8, 10, 12, 14]},
%{avg: 6.4, input: [7, 6, 5, 4, 3, 2, 1, 2, 4, 6, 8, 10, 12, 14, 12]},
%{avg: 6.6, input: [6, 5, 4, 3, 2, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10]},
%{avg: 6.733, input: [5, 4, 3, 2, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10, 8]},
%{avg: 6.8, input: [4, 3, 2, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10, 8, 6]},
%{avg: 6.8, input: [3, 2, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10, 8, 6, 4]},
%{avg: 6.733, input: [2, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10, 8, 6, 4, 2]}]
Erlang
main() ->
SMA3 = sma(3),
SMA5 = sma(5),
Ns = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1],
lists:foreach(
fun (N) ->
io:format("Added ~b, sma(3) -> ~f, sma(5) -> ~f~n",[N,next(SMA3,N),next(SMA5,N)])
end, Ns),
stop(SMA3),
stop(SMA5).
sma(W) ->
{sma,spawn(?MODULE,loop,[W,[]])}.
loop(Window, Numbers) ->
receive
{_Pid, stop} ->
ok;
{Pid, N} when is_number(N) ->
case length(Numbers) < Window of
true ->
Next = Numbers++[N];
false ->
Next = tl(Numbers)++[N]
end,
Pid ! {average, lists:sum(Next)/length(Next)},
loop(Window,Next);
_ ->
ok
end.
stop({sma,Pid}) ->
Pid ! {self(),stop},
ok.
next({sma,Pid},N) ->
Pid ! {self(), N},
receive
{average, Ave} ->
Ave
end.
- Output:
9> sma:main().
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
ok
Erlang has closures, but immutable variables. A solution then is to use processes and a simple message passing based API.
Euler Math Toolbox
Matrix languages have routines to compute the gliding avarages for a given sequence of items.
>n=1000; m=100; x=random(1,n);
>x10=fold(x,ones(1,m)/m);
>x10=fftfold(x,ones(1,m)/m)[m:n]; // more efficientIt is less efficient to loop as in the following commands.
>function store (x:number, v:vector, n:index) ...
$if cols(v)<n then return v|x;
$else
$ v=rotleft(v); v[-1]=x;
$ return v;
$endif;
$endfunction
>v=zeros(1,0); for k=1:20; v=store(k,v,10); mean(v), end;
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
>v
[ 11 12 13 14 15 16 17 18 19 20 ]F#
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 ""
- 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
Factor
The I word creates a quotation (anonymous function) that closes over a sequence and a period. This quotation handles adding/removing numbers to the simple moving average (SMA). We can then add a number to the SMA using sma-add and get the SMA's sequence and mean with sma-query. Quotations adhere to the sequence protocol so we can obtain the sequence of numbers simply by calling first on the SMA quotation.
USING: kernel interpolate io locals math.statistics prettyprint
random sequences ;
IN: rosetta-code.simple-moving-avg
:: I ( P -- quot )
V{ } clone :> v!
[ v swap suffix! P short tail* v! ] ;
: sma-add ( quot n -- quot' ) swap tuck call( x x -- x ) ;
: sma-query ( quot -- avg v ) first concat dup mean swap ;
: simple-moving-average-demo ( -- )
5 I 10 <iota> [
over sma-query unparse
[I After ${2} numbers Sequence is ${0} Mean is ${1}I] nl
100 random sma-add
] each drop ;
MAIN: simple-moving-average-demo
- Output:
After 0 numbers Sequence is V{ } Mean is 0
After 1 numbers Sequence is V{ 41 } Mean is 41
After 2 numbers Sequence is V{ 41 31 } Mean is 36
After 3 numbers Sequence is V{ 41 31 2 } Mean is 24+2/3
After 4 numbers Sequence is V{ 41 31 2 24 } Mean is 24+1/2
After 5 numbers Sequence is V{ 41 31 2 24 70 } Mean is 33+3/5
After 6 numbers Sequence is V{ 31 2 24 70 80 } Mean is 41+2/5
After 7 numbers Sequence is V{ 2 24 70 80 96 } Mean is 54+2/5
After 8 numbers Sequence is V{ 24 70 80 96 84 } Mean is 70+4/5
After 9 numbers Sequence is V{ 70 80 96 84 7 } Mean is 67+2/5
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))
}
}
}- 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
: 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.
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
FreeBASIC
' FB 1.05.0 Win64
Type FuncType As Function(As Double) As Double
' These 'shared' variables are available to all functions defined below
Dim Shared p As UInteger
Dim Shared list() As Double
Function sma(n As Double) As Double
Redim Preserve list(0 To UBound(list) + 1)
list(UBound(list)) = n
Dim start As Integer = 0
Dim length As Integer = UBound(list) + 1
If length > p Then
start = UBound(list) - p + 1
length = p
End If
Dim sum As Double = 0.0
For i As Integer = start To UBound(list)
sum += list(i)
Next
Return sum / length
End Function
Function initSma(period As Uinteger) As FuncType
p = period
Erase list '' ensure the array is empty on each initialization
Return @sma
End Function
Dim As FuncType ma = initSma(3)
Print "Period = "; p
Print
For i As Integer = 0 To 9
Print "Add"; i; " => moving average ="; ma(i)
Next
Print
ma = initSma(5)
Print "Period = "; p
Print
For i As Integer = 9 To 0 Step -1
Print "Add"; i; " => moving average ="; ma(i)
Next
Print
Print "Press any key to quit"
Sleep
- Output:
Period = 3 Add 0 => moving average = 0 Add 1 => moving average = 0.5 Add 2 => moving average = 1 Add 3 => moving average = 2 Add 4 => moving average = 3 Add 5 => moving average = 4 Add 6 => moving average = 5 Add 7 => moving average = 6 Add 8 => moving average = 7 Add 9 => moving average = 8 Period = 5 Add 9 => moving average = 9 Add 8 => moving average = 8.5 Add 7 => moving average = 8 Add 6 => moving average = 7.5 Add 5 => moving average = 7 Add 4 => moving average = 6 Add 3 => moving average = 5 Add 2 => moving average = 4 Add 1 => moving average = 3 Add 0 => moving average = 2
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
Go
package main
import "fmt"
func sma(period int) func(float64) float64 {
var i int
var sum float64
var storage = make([]float64, 0, period)
return func(input float64) (avrg float64) {
if len(storage) < period {
sum += input
storage = append(storage, input)
}
sum += input - storage[i]
storage[i], i = input, (i+1)%period
avrg = sum / float64(len(storage))
return
}
}
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))
}
}
- 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
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)) }
- Output:
1.0 1.5 2.0 2.5 3.0 3.8 4.2 4.2 3.8 3.0
Haskell
Conform version to the requirement, function SMA called multiple times with just a number:
{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Data.List
import Data.IORef
data Pair a b = Pair !a !b
mean :: Fractional a => [a] -> a
mean = divl . foldl' (\(Pair s l) x -> Pair (s+x) (l+1)) (Pair 0.0 0)
where divl (_,0) = 0.0
divl (s,l) = s / fromIntegral l
series = [1,2,3,4,5,5,4,3,2,1]
mkSMA :: Int -> IO (Double -> IO Double)
mkSMA period = avgr <$> newIORef []
where avgr nsref x = readIORef nsref >>= (\ns ->
let xs = take period (x:ns)
in writeIORef nsref xs $> mean xs)
main = mkSMA 3 >>= (\sma3 -> mkSMA 5 >>= (\sma5 ->
mapM_ (str <$> pure n <*> sma3 <*> sma5) series))
where str n mm3 mm5 =
concat ["Next number = ",show n,", SMA_3 = ",show mm3,", SMA_5 = ",show mm5]
- Output:
Next number = 1.0, SMA_3 = 1.0, SMA_5 = 1.0 Next number = 2.0, SMA_3 = 1.5, SMA_5 = 1.5 Next number = 3.0, SMA_3 = 2.0, SMA_5 = 2.0 Next number = 4.0, SMA_3 = 3.0, SMA_5 = 2.5 Next number = 5.0, SMA_3 = 4.0, SMA_5 = 3.0 Next number = 5.0, SMA_3 = 4.666666666666667, SMA_5 = 3.8 Next number = 4.0, SMA_3 = 4.666666666666667, SMA_5 = 4.2 Next number = 3.0, SMA_3 = 4.0, SMA_5 = 4.2 Next number = 2.0, SMA_3 = 3.0, SMA_5 = 3.8 Next number = 1.0, SMA_3 = 2.0, SMA_5 = 3.0
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..]
Stateful function using the state monad to keep track of state
import Control.Monad
import Control.Monad.State
period :: Int
period = 3
type SMAState = [Float]
computeSMA :: Float -> State SMAState Float
computeSMA x = do
previousValues <- get
let values = previousValues ++ [x]
let newAverage = if length values <= period then (sum values) / (fromIntegral $ length remainingValues :: Float)
else (sum remainingValues) / (fromIntegral $ length remainingValues :: Float)
where remainingValues = dropIf period values
put $ dropIf period values
return newAverage
dropIf :: Int -> [a] -> [a]
dropIf x xs = drop ((length xs) - x) xs
demostrateSMA :: State SMAState [Float]
demostrateSMA = mapM computeSMA [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]
main :: IO ()
main = print $ evalState demostrateSMA []
- Output:
[1.0,1.5,2.0,3.0,4.0,4.6666665,4.6666665,4.0,3.0,2.0]
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) )
ENDnum=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
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
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:
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
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:
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
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:
lex =: 1 :'(a[n__a=.m#_.[a=.18!:3$~0)&(4 :''(+/%#)(#~1-128!:5)n__x=.1|.!.y n__x'')'
Example:
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
Here, the &> is analogous to the "for each" of other languages.
Or, a more traditional approach could be used:
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
Java
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 0.0; // 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();
}
}
}
- 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
Using for loop
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));
}
- 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
Using reduce/filter
// single-sided
Array.prototype.simpleSMA=function(N) {
return this.map(
function(el,index, _arr) {
return _arr.filter(
function(x2,i2) {
return i2 <= index && i2 > index - N;
})
.reduce(
function(current, last, index, arr){
return (current + last);
})/index || 1;
});
};
g=[0,1,2,3,4,5,6,7,8,9,10];
console.log(g.simpleSMA(3));
console.log(g.simpleSMA(5));
console.log(g.simpleSMA(g.length));
- Output:
[1, 1, 1.5, 2, 2.25, 2.4, 2.5, 2.5714285714285716, 2.625, 2.6666666666666665, 2.7] [1, 1, 1.5, 2, 2.5, 3, 3.3333333333333335, 3.5714285714285716, 3.75, 3.888888888888889, 4] [1, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5]
jq
Works with jq, the C implementation of jq
Works with gojq, the Go implementation of jq
Works with jaq, the Rust implementation of jq
jq functions are stateless, so in this entry, sma($x) is defined as a parameterized jq filter that takes as input the relevant state as a JSON object. This should initially include a key named "period" specifying the period, which may be infinite, i.e. the jq value `infinite` corresponding to positive infinity.
For example the initial call to sma/1 might look like:
{period: infinite} | sma(100)
Two examples are given, one with a finite and the other with an infinite period. Both compute the average of the 11 numbers 0, 1, ... 10, by calling sma(0) and then sma(1), and so on.
# The input should be a JSON object with a key named "period".
# The output is a JSON object with a key named "average" giving the SMA.
def sma($x):
def average:
.n as $n
| if $n == null or $n == 0 then . + {n: 1, average: $x}
else .average |= (. * $n + $x) / ($n + 1)
| .n += 1
end;
if . == null or (.period and .period < 1)
then "The initial call to sma/1 must specify the period properly" | error
elif .n and .n < 0 then "Invalid value of .n" | error
elif (.period | isinfinite) then average
elif .n == null or .n == 0 then . + {n: 1, average: $x, array: [$x]}
else .n as $n
| if $n < .period
then .array += [$x]
| .n += 1
else .array |= .[1:] + [$x]
end
| .average = (.array | (add/length))
end;
# Call sma($x) for the 11 numbers 0, 1, ... 10.
def example($period):
reduce range(0;11) as $x({period: $period}; sma($x))
| .average ;
example(11), example(infinite)- Output:
5 5
Julia
using Statistics
The function wants specified the type of the data in the buffer and, if you want, the limit of the buffer.
function movingaverage(::Type{T} = Float64; lim::Integer = -1) where T<:Real
buffer = Vector{T}(0)
if lim == -1
# unlimited buffer
return (y::T) -> begin
push!(buffer, y)
return mean(buffer)
end
else
# limited size buffer
return (y) -> begin
push!(buffer, y)
if length(buffer) > lim shift!(buffer) end
return mean(buffer)
end
end
end
test = movingaverage()
@show test(1.0) # mean([1])
@show test(2.0) # mean([1, 2])
@show test(3.0) # mean([1, 2, 3])
- Output:
test(1.0) = 1.0 test(2.0) = 1.5 test(3.0) = 2.0
K
Non-stateful:
v:v,|v:1+!5
v
1 2 3 4 5 5 4 3 2 1
avg:{(+/x)%#x}
sma:{avg'x@(,\!y),(1+!y)+\:!y}
sma[v;5]
1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3
Stateful:
sma:{n::x#_n; {n::1_ n,x; {avg x@&~_n~'x} n}}
sma[5]' v
1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3
Kotlin
// version 1.0.6
fun initMovingAverage(p: Int): (Double) -> Double {
if (p < 1) throw IllegalArgumentException("Period must be a positive integer")
val list = mutableListOf<Double>()
return {
list.add(it)
if (list.size > p) list.removeAt(0)
list.average()
}
}
fun main(args: Array<String>) {
val sma4 = initMovingAverage(4)
val sma5 = initMovingAverage(5)
val numbers = listOf(1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 4.0, 3.0, 2.0, 1.0)
println("num\tsma4\tsma5\n")
for (number in numbers) println("${number}\t${sma4(number)}\t${sma5(number)}")
}
- Output:
num sma4 sma5 1.0 1.0 1.0 2.0 1.5 1.5 3.0 2.0 2.0 4.0 2.5 2.5 5.0 3.5 3.0 5.0 4.25 3.8 4.0 4.5 4.2 3.0 4.25 4.2 2.0 3.5 3.8 1.0 2.5 3.0
Lasso
define simple_moving_average(a::array,s::integer)::decimal => {
#a->size == 0 ? return 0.00
#s == 0 ? return 0.00
#a->size == 1 ? return decimal(#a->first)
#s == 1 ? return decimal(#a->last)
local(na = array)
if(#a->size <= #s) => {
#na = #a
else
local(ar = #a->ascopy)
#ar->reverse
loop(#s) => { #na->insert(#ar->get(loop_count)) }
}
#s > #na->size ? #s = #na->size
return (with e in #na sum #e) / decimal(#s)
}
// tests:
'SMA 3 on array(1,2,3,4,5,5,4,3,2,1): '
simple_moving_average(array(1,2,3,4,5,5,4,3,2,1),3)
'\rSMA 5 on array(1,2,3,4,5,5,4,3,2,1): '
simple_moving_average(array(1,2,3,4,5,5,4,3,2,1),5)
'\r\rFurther example: \r'
local(mynumbers = array, sma_num = 5)
loop(10) => {^
#mynumbers->insert(integer_random(1,100))
#mynumbers->size + ' numbers: ' + #mynumbers
' SMA3 is: ' + simple_moving_average(#mynumbers,3)
', SMA5 is: ' + simple_moving_average(#mynumbers,5)
'\r'
^}
- Output:
SMA 3 on array(1,2,3,4,5,5,4,3,2,1): 2.000000 SMA 5 on array(1,2,3,4,5,5,4,3,2,1): 3.000000 Further example: 1 numbers: array(91) SMA3 is: 91.000000, SMA5 is: 91.000000 2 numbers: array(91, 30) SMA3 is: 60.500000, SMA5 is: 60.500000 3 numbers: array(91, 30, 99) SMA3 is: 73.333333, SMA5 is: 73.333333 4 numbers: array(91, 30, 99, 73) SMA3 is: 67.333333, SMA5 is: 73.250000 5 numbers: array(91, 30, 99, 73, 22) SMA3 is: 64.666667, SMA5 is: 63.000000 6 numbers: array(91, 30, 99, 73, 22, 35) SMA3 is: 43.333333, SMA5 is: 51.800000 7 numbers: array(91, 30, 99, 73, 22, 35, 93) SMA3 is: 50.000000, SMA5 is: 64.400000 8 numbers: array(91, 30, 99, 73, 22, 35, 93, 24) SMA3 is: 50.666667, SMA5 is: 49.400000 9 numbers: array(91, 30, 99, 73, 22, 35, 93, 24, 8) SMA3 is: 41.666667, SMA5 is: 36.400000 10 numbers: array(91, 30, 99, 73, 22, 35, 93, 24, 8, 80) SMA3 is: 37.333333, SMA5 is: 48.000000
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
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 functionLogo
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.
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]If namespace pollution is a concern, UCB Logo supplies a GENSYM command to obtain unique names in order to avoid collisions.
...
localmake "qn word :name gensym
...
; list user-defined functions and variables
show procedures ; [average avg3 make.sma]
show names ; [[[] [avg3.g1]]Lua
function sma(period)
local t = {}
function sum(t)
sum = 0
for _, v in ipairs(t) do
sum = sum + v
end
return sum
end
function average(n)
if #t == period then table.remove(t, 1) end
t[#t + 1] = n
return sum(t) / #t
end
return average
end
sma5 = sma(5)
sma10 = sma(10)
print("SMA 5")
for v=1,15 do print(sma5(v)) end
print("\nSMA 10")
for v=1,15 do print(sma10(v)) end
Mathematica / Wolfram Language
This version uses a list entry so it can use the built-in function.
MA[x_List, r_] := Join[Table[Mean[x[[1;;y]]],{y,r-1}], MovingAverage[x,r]]
This version is stateful instead.
MAData = {{}, 0};
MAS[x_, t_: Null] :=
With[{r = If[t === Null, MAData[[2]], t]},
Mean[MAData[[1]] =
If[Length[#] > (MAData[[2]] = r), #[[-r ;; -1]], #] &@
Append[MAData[[1]], x]]]
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)
[m,z] = filter(ones(1,P),P,x);
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.
[m,z] = filter(ones(1,P),P,x,z);
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:
% 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)).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.
MiniScript
We define an SMA class, which can be configured with the desired window size (P).
SMA = {}
SMA.P = 5 // (a default; may be overridden)
SMA.buffer = null
SMA.next = function(n)
if self.buffer == null then self.buffer = []
self.buffer.push n
if self.buffer.len > self.P then self.buffer.pull
return self.buffer.sum / self.buffer.len
end function
sma3 = new SMA
sma3.P = 3
sma5 = new SMA
for i in range(10)
num = round(rnd*100)
print "num: " + num + " sma3: " + sma3.next(num) + " sma5: " + sma5.next(num)
end for
- Output:
num: 81 sma3: 81 sma5: 81 num: 82 sma3: 81.5 sma5: 81.5 num: 78 sma3: 80.333333 sma5: 80.333333 num: 54 sma3: 71.333333 sma5: 73.75 num: 94 sma3: 75.333333 sma5: 77.8 num: 8 sma3: 52 sma5: 63.2 num: 40 sma3: 47.333333 sma5: 54.8 num: 98 sma3: 48.666667 sma5: 58.8 num: 48 sma3: 62 sma5: 57.6 num: 41 sma3: 62.333333 sma5: 47 num: 94 sma3: 61 sma5: 64.2
NetRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 20
class RAvgSimpleMoving public
properties private
window = java.util.Queue
period
sum
properties constant
exMsg = 'Period must be a positive integer'
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method RAvgSimpleMoving(period_) public
if \period_.datatype('w') then signal RuntimeException(exMsg)
if period_ <= 0 then signal RuntimeException(exMsg)
window = LinkedList()
period = period_
sum = 0
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method newNum(num) public
sum = sum + num
window.add(num)
if window.size() > period then do
rmv = (Rexx window.remove())
sum = sum - rmv
end
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getAvg() public returns Rexx
if window.isEmpty() then do
avg = 0
end
else do
avg = sum / window.size()
end
return avg
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method run_samples(args = String[]) public static
testData = [Rexx 1, 2, 3, 4, 5, 5, 4, 3, 2, 1]
windowSizes = [Rexx 3, 5]
loop windSize over windowSizes
ma = RAvgSimpleMoving(windSize)
loop xVal over testData
ma.newNum(xVal)
say 'Next number =' xVal.right(5)', SMA =' ma.getAvg().format(10, 9)
end xVal
say
end windSize
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method main(args = String[]) public static
run_samples(args)
return
- Output:
Next number = 1.0, SMA = 1.000000000 Next number = 2.0, SMA = 1.500000000 Next number = 3.0, SMA = 2.000000000 Next number = 4.0, SMA = 3.000000000 Next number = 5.0, SMA = 4.000000000 Next number = 5.0, SMA = 4.666666667 Next number = 4.0, SMA = 4.666666667 Next number = 3.0, SMA = 4.000000000 Next number = 2.0, SMA = 3.000000000 Next number = 1.0, SMA = 2.000000000 Next number = 1.0, SMA = 1.000000000 Next number = 2.0, SMA = 1.500000000 Next number = 3.0, SMA = 2.000000000 Next number = 4.0, SMA = 2.500000000 Next number = 5.0, SMA = 3.000000000 Next number = 5.0, SMA = 3.800000000 Next number = 4.0, SMA = 4.200000000 Next number = 3.0, SMA = 4.200000000 Next number = 2.0, SMA = 3.800000000 Next number = 1.0, SMA = 3.000000000
Nim
import deques
proc simplemovingaverage(period: int): auto =
assert period > 0
var
summ, n = 0.0
values: Deque[float]
for i in 1..period:
values.addLast(0)
proc sma(x: float): float =
values.addLast(x)
summ += x - values.popFirst()
n = min(n+1, float(period))
result = summ / n
return sma
var sma = simplemovingaverage(3)
for i in 1..5: echo sma(float(i))
for i in countdown(5,1): echo sma(float(i))
echo ""
var sma2 = simplemovingaverage(5)
for i in 1..5: echo sma2(float(i))
for i in countdown(5,1): echo sma2(float(i))
- Output:
1.0 1.5 2.0 3.0 4.0 4.666666666666667 4.666666666666667 4.0 3.0 2.0 1.0 1.5 2.0 2.5 3.0 3.8 4.2 4.2 3.8 3.0
Objeck
use Collection;
class MovingAverage {
@window : FloatQueue;
@period : Int;
@sum : Float;
New(period : Int) {
@window := FloatQueue->New();
@period := period;
}
method : NewNum(num : Float) ~ Nil {
@sum += num;
@window->Add(num);
if(@window->Size() > @period) {
@sum -= @window->Remove();
};
}
method : GetAvg() ~ Float {
if(@window->IsEmpty()) {
return 0; # technically the average is undefined
};
return @sum / @window->Size();
}
function : Main(args : String[]) ~ Nil {
testData := [1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 4.0, 3.0, 2.0, 1.0];
windowSizes := [3.0, 5.0];
each(i : windowSizes) {
windSize := windowSizes[i];
ma := MovingAverage->New(windSize);
each(j : testData) {
x := testData[j];
ma->NewNum(x);
avg := ma->GetAvg();
"Next number = {$x}, SMA = {$avg}"->PrintLine();
};
IO.Console->PrintLine();
};
}
}- Output:
Next number = 1.0, SMA = 1.0 Next number = 2.0, SMA = 1.500 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 = 4.667 Next number = 4.0, SMA = 4.667 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 = 1.500 Next number = 3.0, SMA = 2.0 Next number = 4.0, SMA = 2.500 Next number = 5.0, SMA = 3.0 Next number = 5.0, SMA = 3.800 Next number = 4.0, SMA = 4.200 Next number = 3.0, SMA = 4.200 Next number = 2.0, SMA = 3.800 Next number = 1.0, SMA = 3.0
Objective-C
#import <Foundation/Foundation.h>
@interface MovingAverage : NSObject {
unsigned int period;
NSMutableArray *window;
double sum;
}
- (instancetype)initWithPeriod:(unsigned int)thePeriod;
@end
@implementation MovingAverage
// init with default period
- (instancetype)init {
self = [super init];
if(self) {
period = 10;
window = [[NSMutableArray alloc] init];
sum = 0.0;
}
return self;
}
// init with specified period
- (instancetype)initWithPeriod:(unsigned int)thePeriod {
self = [super init];
if(self) {
period = thePeriod;
window = [[NSMutableArray alloc] init];
sum = 0.0;
}
return self;
}
// add a new number to the window
- (void)add:(double)val {
sum += val;
[window addObject:@(val)];
if([window count] > period) {
NSNumber *n = window[0];
sum -= [n doubleValue];
[window removeObjectAtIndex:0];
}
}
// get the average value
- (double)avg {
if([window count] == 0) {
return 0; // technically the average is undefined
}
return sum / [window count];
}
// set the period, resizes current window
- (void)setPeriod:(unsigned int)thePeriod {
// make smaller?
if(thePeriod < [window count]) {
for(int i = 0; i < thePeriod; ++i) {
NSNumber *n = window[0];
sum -= [n doubleValue];
[window removeObjectAtIndex:0];
}
}
period = thePeriod;
}
// get the period (window size)
- (unsigned int)period {
return period;
}
// clear the window and current sum
- (void)clear {
[window removeAllObjects];
sum = 0;
}
@end
int main (int argc, const char * argv[]) {
@autoreleasepool {
double testData[10] = {1,2,3,4,5,5,4,3,2,1};
int periods[2] = {3,5};
for(int i = 0; i < 2; ++i) {
MovingAverage *ma = [[MovingAverage alloc] initWithPeriod:periods[i]];
for(int j = 0; j < 10; ++j) {
[ma add:testData[j]];
NSLog(@"Next number = %f, SMA = %f", testData[j], [ma avg]);
}
NSLog(@"\n");
}
}
return 0;
}
- Output:
Next number = 1.000000, SMA = 1.000000 Next number = 2.000000, SMA = 1.500000 Next number = 3.000000, SMA = 2.000000 Next number = 4.000000, SMA = 3.000000 Next number = 5.000000, SMA = 4.000000 Next number = 5.000000, SMA = 4.666667 Next number = 4.000000, SMA = 4.666667 Next number = 3.000000, SMA = 4.000000 Next number = 2.000000, SMA = 3.000000 Next number = 1.000000, SMA = 2.000000 Next number = 1.000000, SMA = 1.000000 Next number = 2.000000, SMA = 1.500000 Next number = 3.000000, SMA = 2.000000 Next number = 4.000000, SMA = 2.500000 Next number = 5.000000, SMA = 3.000000 Next number = 5.000000, SMA = 3.800000 Next number = 4.000000, SMA = 4.200000 Next number = 3.000000, SMA = 4.200000 Next number = 2.000000, SMA = 3.800000 Next number = 1.000000, SMA = 3.000000
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
- 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:
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
Oforth
createSMA returns a closure. The list of values is included into a channel so this code is thread-safe : multiple tasks running in parallel can call the closure returned.
import: parallel
: createSMA(period)
| ch |
Channel new [ ] over send drop ->ch
#[ ch receive + left(period) dup avg swap ch send drop ] ;Usage:
: test
| sma3 sma5 l |
3 createSMA -> sma3
5 createSMA -> sma5
[ 1, 2, 3, 4, 5, 5, 4, 3, 2, 1 ] ->l
"SMA3" .cr l apply( #[ sma3 perform . ] ) printcr
"SMA5" .cr l apply( #[ sma5 perform . ] ) ;- Output:
>test SMA3 1 1.5 2 3 4 4.66666666666667 4.66666666666667 4 3 2 SMA5 1 1.5 2 2.5 3 3.8 4.2 4.2 3.8 3 ok
ooRexx
ooRexx does not have stateful functions, but the same effect can be achieved by using object instances.
testdata = .array~of(1, 2, 3, 4, 5, 5, 4, 3, 2, 1)
-- run with different period sizes
loop period over .array~of(3, 5)
say "Period size =" period
say
movingaverage = .movingaverage~new(period)
loop number over testdata
average = movingaverage~addnumber(number)
say " Next number =" number", moving average =" average
end
say
end
::class movingaverage
::method init
expose period queue sum
use strict arg period
sum = 0
-- the circular queue makes this easy
queue = .circularqueue~new(period)
-- add a number to the average set
::method addNumber
expose queue sum
use strict arg number
sum += number
-- add this to the queue
old = queue~queue(number)
-- if we pushed an element off the end of the queue,
-- subtract this from our sum
if old \= .nil then sum -= old
-- and return the current item
return sum / queue~items
-- extra method to retrieve current average
::method average
expose queue sum
-- undefined really, but just return 0
if queue~isempty then return 0
-- return current queue
return sum / queue~items
- Output:
Period size = 3 Next number = 1, moving average = 1 Next number = 2, moving average = 1.5 Next number = 3, moving average = 2 Next number = 4, moving average = 3 Next number = 5, moving average = 4 Next number = 5, moving average = 4.66666667 Next number = 4, moving average = 4.66666667 Next number = 3, moving average = 4 Next number = 2, moving average = 3 Next number = 1, moving average = 2 Period size = 5 Next number = 1, moving average = 1 Next number = 2, moving average = 1.5 Next number = 3, moving average = 2 Next number = 4, moving average = 2.5 Next number = 5, moving average = 3 Next number = 5, moving average = 3.8 Next number = 4, moving average = 4.2 Next number = 3, moving average = 4.2 Next number = 2, moving average = 3.8 Next number = 1, moving average = 3
OxygenBasic
def max 1000
Class MovingAverage
'==================
indexbase 1
double average,invperiod,mdata[max]
sys index,period
method Setup(double a,p)
sys i
Period=p
invPeriod=1/p
index=0
average=a
for i=1 to period
mdata[i]=a
next
end method
method Data(double v) as double
sys i
index++
if index>period then index=1 'recycle
i=index+1 'for oldest data
if i>period then i=1 'recycle
mdata[index]=v
average=average+invperiod*(v-mdata[i])
end method
end class
'TEST
'====
MovingAverage A
A.Setup 100,10 'initial value and period
A.data 50
'...
print A.average 'reult 95Oz
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
endPARI/GP
Partial implementation: does not (yet?) create different stores on each invocation.
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
};Pascal
Like in other implementations the sum of the last p values is only updated by subtracting the oldest value and addindg the new. To minimize rounding errors after p values the sum is corrected to the real sum.
program sma;
type
tsma = record
smaValue : array of double;
smaAverage,
smaSumOld,
smaSumNew,
smaRezActLength : double;
smaActLength,
smaLength,
smaPos :NativeInt;
smaIsntFull: boolean;
end;
procedure smaInit(var sma:tsma;p: NativeUint);
Begin
with sma do
Begin
setlength(smaValue,0);
setlength(smaValue,p);
smaLength:= p;
smaActLength := 0;
smaAverage:= 0.0;
smaSumOld := 0.0;
smaSumNew := 0.0;
smaPos := p-1;
smaIsntFull := true
end;
end;
function smaAddValue(var sma:tsma;v: double):double;
Begin
with sma do
Begin
IF smaIsntFull then
Begin
inc(smaActLength);
smaRezActLength := 1/smaActLength;
smaIsntFull := smaActLength < smaLength ;
end;
smaSumOld := smaSumOld+v-smaValue[smaPos];
smaValue[smaPos] := v;
smaSumNew := smaSumNew+v;
smaPos := smaPos-1;
if smaPos < 0 then
begin
smaSumOld:= smaSumNew;
smaSumNew:= 0.0;
smaPos := smaLength-1;
end;
smaAverage := smaSumOld *smaRezActLength;
smaAddValue:= smaAverage;
end;
end;
var
sma3,sma5:tsma;
i : LongInt;
begin
smaInit(sma3,3);
smaInit(sma5,5);
For i := 1 to 5 do
Begin
write('Inserting ',i,' into sma3 ',smaAddValue(sma3,i):0:4);
writeln(' Inserting ',i,' into sma5 ',smaAddValue(sma5,i):0:4);
end;
For i := 5 downto 1 do
Begin
write('Inserting ',i,' into sma3 ',smaAddValue(sma3,i):0:4);
writeln(' Inserting ',i,' into sma5 ',smaAddValue(sma5,i):0:4);
end;
//speed test
smaInit(sma3,3);
For i := 1 to 100000000 do
smaAddValue(sma3,i);
writeln('100''000''000 insertions ',sma3.smaAverage:0:4);
end.
- output
time ./sma
Inserting 1 into sma3 1.0000 Inserting 1 into sma5 1.0000
Inserting 2 into sma3 1.5000 Inserting 2 into sma5 1.5000
Inserting 3 into sma3 2.0000 Inserting 3 into sma5 2.0000
Inserting 4 into sma3 3.0000 Inserting 4 into sma5 2.5000
Inserting 5 into sma3 4.0000 Inserting 5 into sma5 3.0000
Inserting 5 into sma3 4.6667 Inserting 5 into sma5 3.8000
Inserting 4 into sma3 4.6667 Inserting 4 into sma5 4.2000
Inserting 3 into sma3 4.0000 Inserting 3 into sma5 4.2000
Inserting 2 into sma3 3.0000 Inserting 2 into sma5 3.8000
Inserting 1 into sma3 2.0000 Inserting 1 into sma5 3.0000
100'000'000 insertions 99999999.0000
real 0m0.780s { 64-Bit }
Perl
Using an initializer function which returns an anonymous closure which closes over an instance (separate for each call to the initializer!) of the lexical variables $period, @list, and $sum:
sub sma_generator {
my $period = shift;
my (@list, $sum);
return sub {
my $number = shift;
push @list, $number;
$sum += $number;
$sum -= shift @list if @list > $period;
return $sum / @list;
}
}
# Usage:
my $sma = sma_generator(3);
for (1, 2, 3, 2, 7) {
printf "append $_ --> sma = %.2f (with period 3)\n", $sma->($_);
}
- Output:
append 1 --> sma = 1.00 (with period 3) append 2 --> sma = 1.50 (with period 3) append 3 --> sma = 2.00 (with period 3) append 2 --> sma = 2.33 (with period 3) append 7 --> sma = 4.00 (with period 3)
Phix
First create a separate file sma.e to encapsulate the private variables. Note in particular the complete lack of any special magic/syntax: it is just a table with some indexes.
with javascript_semantics sequence sma = {} -- ((period,history,circnxt)) (private to sma.e) integer sma_free = 0 global function new_sma(integer period) integer res if sma_free then res = sma_free sma_free = sma[sma_free] sma[res] = {period,{},0} else sma = append(sma,{period,{},0}) res = length(sma) end if return res end function global procedure add_sma(integer sidx, atom val) integer period, circnxt sequence history {period,history,circnxt} = sma[sidx] sma[sidx][2] = 0 -- (kill refcount) if length(history)<period then history = append(history,val) else circnxt += 1 if circnxt>period then circnxt = 1 end if sma[sidx][3] = circnxt history[circnxt] = val end if sma[sidx][2] = history end procedure global function get_sma_average(integer sidx) sequence history = sma[sidx][2] integer l = length(history) if l=0 then return 0 end if return sum(history)/l end function global function moving_average(integer sidx, atom val) add_sma(sidx,val) return get_sma_average(sidx) end function global procedure free_sma(integer sidx) sma[sidx] = sma_free sma_free = sidx end procedure
and the main file is:
with javascript_semantics include sma.e constant sma3 = new_sma(3) constant sma5 = new_sma(5) constant s = {1,2,3,4,5,5,4,3,2,1} integer si for i=1 to length(s) do si = s[i] printf(1,"%2g: sma3=%8g, sma5=%8g\n",{si,moving_average(sma3,si),moving_average(sma5,si)}) end for
- 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= 4.66667, sma5= 3.8 4: sma3= 4.66667, sma5= 4.2 3: sma3= 4, sma5= 4.2 2: sma3= 3, sma5= 3.8 1: sma3= 2, sma5= 3
Picat
main =>
L=[1, 2, 3, 4, 5, 5, 4, 3, 2, 1],
Map3 = new_map([p=3]),
Map5 = new_map([p=5]),
foreach(N in L)
printf("n: %-2d sma3: %-17w sma5: %-17w\n",N, sma(N,Map3), sma(N,Map5))
end.
sma(N,Map) = Average =>
Stream = Map.get(stream,[]) ++ [N],
if Stream.len > Map.get(p) then
Stream := Stream.tail
end,
Average = cond(Stream.len == 0,
0,
sum(Stream) / Stream.len),
Map.put(stream,Stream).- Output:
n: 1 sma3: 1.0 sma5: 1.0 n: 2 sma3: 1.5 sma5: 1.5 n: 3 sma3: 2.0 sma5: 2.0 n: 4 sma3: 3.0 sma5: 2.5 n: 5 sma3: 4.0 sma5: 3.0 n: 5 sma3: 4.666666666666667 sma5: 3.8 n: 4 sma3: 4.666666666666667 sma5: 4.2 n: 3 sma3: 4.0 sma5: 4.2 n: 2 sma3: 3.0 sma5: 3.8 n: 1 sma3: 2.0 sma5: 3.0
PicoLisp
(de sma (@Len)
(curry (@Len (Data)) (N)
(push 'Data N)
(and (nth Data @Len) (con @)) # Truncate
(*/ (apply + Data) (length Data)) ) )(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) ) )- 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
PL/I
version 1
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;version 2
*process source attributes xref;
mat: Proc Options(main);
Dcl a(10) Dec Fixed(8,6);
Dcl s Dec Fixed(10,8);
Dcl n Bin Fixed(31) init(hbound(a)); /* number of items in the list. */
Dcl p Bin Fixed(31) init(3); /* the 1st period */
Dcl q Bin Fixed(31) init(5); /* the 2nd period */
Dcl m Bin Fixed(31);
Call i(a);
Put Edit(' SMA with SMA with',
' number period 3 period 5',
' -------- ---------- ----------')
(Skip,a);
Do m=1 To n;
Put Edit(m,sma(p,m),sma(q,m))(Skip,f(5),2(f(13,6)));
End;
i: Proc(a);
Dcl a(*) Dec Fixed(8,6);
Dcl (j,m) Bin Fixed(31);
Do j=1 To hbound(a)/2;
a(j)=j; /* ··· increasing values. */
End;
Do k=hbound(a)/2 To 1 By -1;
a(j)=k; /* ··· decreasing values. */
j+=1;
End;
End;
sma: Proc(p,j) Returns(Dec Fixed(8,6));
Dcl s Dec fixed(8,6) Init(0);
Dcl i Bin Fixed(31) Init(0);
Dcl j Bin Fixed(31) Init((hbound(a)+1));
Dcl (p,i,k,ka,kb) Bin Fixed(31);
ka=max(1,j-p+1);
kb=j+p;
Do k=ka To kb While(k<=j);
i+=1;
s+=a(k)
End;
s=s/i+0.5e-6;
Return(s);
End;
End;- Output:
SMA with SMA with
number period 3 period 5
-------- ---------- ----------
1 1.000000 1.000000
2 1.500000 1.500000
3 2.000000 2.000000
4 3.000000 2.500000
5 4.000000 3.000000
6 4.666667 3.800000
7 4.666667 4.200000
8 4.000000 4.200000
9 3.000000 3.800000
10 2.000000 3.000000
Pony
class MovingAverage
let period: USize
let _arr: Array[I32] // circular buffer
var _curr: USize // index of pointer position
var _total: I32 // cache the total so far
new create(period': USize) =>
period = period'
_arr = Array[I32](period) // preallocate space
_curr = 0
_total = 0
fun ref apply(n: I32): F32 =>
_total = _total + n
if _arr.size() < period then
_arr.push(n)
else
try
let prev = _arr.update(_curr, n)?
_total = _total - prev
_curr = (_curr + 1) % period
end
end
_total.f32() / _arr.size().f32()
// ---- TESTING -----
actor Main
new create(env: Env) =>
let foo = MovingAverage(3)
let bar = MovingAverage(5)
let data: Array[I32] = [1; 2; 3; 4; 5; 5; 4; 3; 2; 1]
for v in data.values() do
env.out.print("Foo: " + foo(v).string())
end
for v in data.values() do
env.out.print("Bar: " + bar(v).string())
end
PowerShell
#This version allows a user to enter numbers one at a time to figure this into the SMA calculations
$inputs = @() #Create an array to hold all inputs as they are entered.
$period1 = 3 #Define the periods you want to utilize
$period2 = 5
Write-host "Enter numbers to observe their moving averages." -ForegroundColor Green
function getSMA ($inputs, [int]$period) #Function takes a array of entered values and a period (3 and 5 in this case)
{
if($inputs.Count -lt $period){$period = $inputs.Count} #Makes sure that if there's less numbers than the designated period (3 in this case), the number of availble values is used as the period instead.
for($count = 0; $count -lt $period; $count++) #Loop sums the latest available values
{
$result += $inputs[($inputs.Count) - $count - 1]
}
return ($result | ForEach-Object -begin {$sum=0 }-process {$sum+=$_} -end {$sum/$period}) #Gets the average for a given period
}
while($true) #Infinite loop so the user can keep entering numbers
{
try{$inputs += [decimal] (Read-Host)}catch{Write-Host "Enter only numbers" -ForegroundColor Red} #Enter the numbers. Error checking to help mitigate bad inputs (non-number values)
"Added " + $inputs[(($inputs.Count) - 1)] + ", sma($period1) = " + (getSMA $inputs $Period1) + ", sma($period2) = " + (getSMA $inputs $period2)
}
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
Python
Both implementations use the deque datatype.
Procedural
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
Class based
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
Tests
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)))
- 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
Quackery
[ $ "bigrat.qky" loadfile ] now!
[ over size -
space swap of
join ] is pad ( $ n --> $ )
[ ' [ stack [ ] ]
copy nested
' [ tuck take swap join
dup size ] join
swap join
' [ > if
[ 1 split nip ]
tuck swap put
0 over witheach +
swap size
dip n->v n->v v/ ]
join copy ] is make-sma ( n --> [ )
( behaviour of [ is: n --> n/d )
[ stack ] is sma-3 ( --> s )
3 make-sma sma-3 put
[ stack ] is sma-5 ( --> s )
5 make-sma sma-5 put
say "n sma-3 sma-5" cr cr
' [ 1 2 3 4 5 5 4 3 2 1 ]
witheach
[ dup echo sp
dup sma-3 share do
7 point$ 10 pad echo$ sp
sma-5 share do
7 point$ 10 pad echo$ cr ]- Output:
n sma-3 sma-5 1 1 1 2 1.5 1.5 3 2 2 4 3 2.5 5 4 3 5 4.6666667 3.8 4 4.6666667 4.2 3 4 4.2 2 3 3.8 1 2 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.
#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
Racket
#lang racket
(require data/queue)
(define (simple-moving-average period)
(define queue (make-queue))
(define sum 0.0)
(lambda (x)
(enqueue! queue x)
(set! sum (+ sum x))
(when (> (queue-length queue) period)
(set! sum (- sum (dequeue! queue))))
(/ sum (queue-length queue))))
;; Tests
(define sma3 (simple-moving-average 3))
(define sma5 (simple-moving-average 5))
(for/lists (lst1 lst2)
([i '(1 2 3 4 5 5 4 3 2 1)])
(values (sma3 i) (sma5 i)))
Raku
(formerly Perl 6)
sub sma-generator (Int $P where * > 0) {
sub ($x) {
state @a = 0 xx $P;
@a.push($x).shift;
@a.sum / $P;
}
}
# Usage:
my &sma = sma-generator 3;
for 1, 2, 3, 2, 7 {
printf "append $_ --> sma = %.2f (with period 3)\n", sma $_;
}
- Output:
append 1 --> sma = 0.33 (with period 3) append 2 --> sma = 1.00 (with period 3) append 3 --> sma = 2.00 (with period 3) append 2 --> sma = 2.33 (with period 3) append 7 --> sma = 4.00 (with period 3)
REXX
The same list of numbers was used as in the ALGOL68 example.
The 1st and 2nd periods (number of values) were parametrized, as well as the total number of values.
/*REXX program illustrates and displays a simple moving average using a constructed list*/
parse arg p q n . /*obtain optional arguments from the CL*/
if p=='' | p=="," then p= 3 /*Not specified? Then use the default.*/
if q=='' | q=="," then q= 5 /* " " " " " " */
if n=='' | n=="," then n= 10 /* " " " " " " */
@.= 0 /*default value, only needed for odd N.*/
do j=1 for n%2; @.j= j /*build 1st half of list, increasing #s*/
end /*j*/
do k=n%2 by -1 to 1; @.j= k; j= j+1 /* " 2nd " " " decreasing " */
end /*k*/
say ' number ' " SMA with period" p' ' " SMA with period" q
say ' ──────── ' "───────────────────" '───────────────────'
pad=' '
do m=1 for n; say center(@.m, 10) pad left(SMA(p, m), 19) left(SMA(q, m), 19)
end /*m*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
SMA: procedure expose @.; parse arg p,j; i= 0 ; $= 0
do k=max(1, j-p+1) to j+p for p while k<=j; i= i + 1; $= $ + @.k
end /*k*/
return $/i /*SMA ≡ simple moving average. */
- output when using the generated default input numbers:
number SMA with period 3 SMA with period 5
──────── ─────────────────── ───────────────────
1 1 1
2 1.5 1.5
3 2 2
4 3 2.5
5 4 3
5 4.66666667 3.8
4 4.66666667 4.2
3 4 4.2
2 3 3.8
1 2 3
Ring
version 1
load "stdlib.ring"
decimals(8)
maxperiod = 20
nums = newlist(maxperiod,maxperiod)
accum = list(maxperiod)
index = list(maxperiod)
window = list(maxperiod)
for i = 1 to maxperiod
index[i] = 1
accum[i] = 0
window[i] = 0
next
for i = 1 to maxperiod
for j = 1 to maxperiod
nums[i][j] = 0
next
next
for n = 1 to 5
see "number = " + n + " sma3 = " + left((string(sma(n,3)) + " "),9) + " sma5 = " + sma(n,5) + nl
next
for n = 5 to 1 step -1
see "number = " + n + " sma3 = " + left((string(sma(n,3)) + " "),9) + " sma5 = " + sma(n,5) + nl
next
see nl
func sma number, period
accum[period] += number - nums[period][index[period]]
nums[period][index[period]] = number
index[period]= (index[period] + 1) % period + 1
if window[period]<period window[period] += 1 ok
return (accum[period] / window[period])Output:
number = 1 sma3 = 1 sma5 = 1 number = 2 sma3 = 1.5000000 sma5 = 1.50000000 number = 3 sma3 = 2 sma5 = 2 number = 4 sma3 = 3 sma5 = 2.50000000 number = 5 sma3 = 4 sma5 = 3 number = 5 sma3 = 4.6666666 sma5 = 3.80000000 number = 4 sma3 = 4.6666666 sma5 = 4.20000000 number = 3 sma3 = 4 sma5 = 4.20000000 number = 2 sma3 = 3 sma5 = 3.80000000 number = 1 sma3 = 2 sma5 = 3
version 2
load "stdlib.ring"
decimals(8)
maxperiod = 20
nums = newlist(maxperiod,maxperiod)
accum = list(maxperiod)
index = list(maxperiod)
window = list(maxperiod)
for i = 1 to maxperiod
index[i] = 1
accum[i] = 0
window[i] = 0
next
for i = 1 to maxperiod
for j = 1 to maxperiod
nums[i][j] = 0
next
next
for n = 1 to 5
see "number = " + n + " sma3 = " + left((string(sma(n,3)) + " "),9) + " sma5 = " + sma(n,5) + nl
next
for n = 5 to 1 step -1
see "number = " + n + " sma3 = " + left((string(sma(n,3)) + " "),9) + " sma5 = " + sma(n,5) + nl
next
see nl
func sma number, period
accum[period] += number - nums[period][index[period]]
nums[period][index[period]] = number
index[period]= (index[period] + 1) % period + 1
if window[period]<period window[period] += 1 ok
return (accum[period] / window[period])Output:
number = 1 sma3 = 1 sma5 = 1 number = 2 sma3 = 1.5000000 sma5 = 1.50000000 number = 3 sma3 = 2 sma5 = 2 number = 4 sma3 = 3 sma5 = 2.50000000 number = 5 sma3 = 4 sma5 = 3 number = 5 sma3 = 4.6666666 sma5 = 3.80000000 number = 4 sma3 = 4.6666666 sma5 = 4.20000000 number = 3 sma3 = 4 sma5 = 4.20000000 number = 2 sma3 = 3 sma5 = 3.80000000 number = 1 sma3 = 2 sma5 = 3
version 3
### RING: Function Moving Average. Bert Mariani 2016-06-22
###------------------------------
### Data array of Google prices
aGOOGPrices = ["658","675","670","664","664","663","663","662","675","693","689","675",
"636","633","632","607","607","617","617","581","593","570","574","571","575","596",
"596","601","583","635","587","574","552","531","536","502","488","482","490","503",
"507","521","534","525","534","559","552","554","555","555","552","579","580","577",
"575","562","560","559","558","569","573","577","574","559","552","553","560","569",
"582","579","593","598","593","598","593","586","602","591","594","595","603","614",
"620","625","635","627","632","631","620","626","616","606","602","659","683","671",
"670","659","673","679"]
###-------------------------------------------------------------
### CALL the Function: MovingAverage arrayOfPrices timePeriod
aGOOGMvgAvg = MovingAverage( aGOOGPrices, 10 )
aGOOGMvgAvg = MovingAverage( aGOOGPrices, 30 )
###-------------------------------------------------------------
### FUNCTION: MovingAverage
Func MovingAverage arrayPrices, timePeriod
arrayMvgAvg = [] ### Output Results to this array
z = len(arrayPrices) ### array data length
sumPrices = 0
###--------------------------------
### First MAvg Sum 1 to timePeriod
###--------------------------------
for i = 1 to timePeriod
sumPrices = sumPrices + arrayPrices[i]
mvgAvg = sumPrices / i
Add( arrayMvgAvg, mvgAvg)
next
###-----------------------------------------------
### Second MAvg Sum timePeriod +1 to End of Data
###-----------------------------------------------
for i = timePeriod + 1 to z
sumPrices = sumPrices - arrayPrices[i-timePeriod] + arrayPrices[i]
mvgAvg = sumPrices / timePeriod
Add (arrayMvgAvg, mvgAvg
next
return arrayMvgAvg
###-------------------------------------------------------------
OUTPUT Google Prices moving average using timePeriod = 10
Index 88 CurPrice 631 Sum 17735 MvgAvg 591.17
Index 89 CurPrice 620 Sum 17797 MvgAvg 593.23
Index 90 CurPrice 626 Sum 17854 MvgAvg 595.13
Index 91 CurPrice 616 Sum 17897 MvgAvg 596.57
Index 92 CurPrice 606 Sum 17926 MvgAvg 597.53
Index 93 CurPrice 602 Sum 17954 MvgAvg 598.47
Index 94 CurPrice 659 Sum 18054 MvgAvg 601.80
Index 95 CurPrice 683 Sum 18185 MvgAvg 606.17
Index 96 CurPrice 671 Sum 18303 MvgAvg 610.10
Index 97 CurPrice 670 Sum 18413 MvgAvg 613.77
Index 98 CurPrice 659 Sum 18503 MvgAvg 616.77
Index 99 CurPrice 673 Sum 18594 MvgAvg 619.80
Index 100 CurPrice 679 Sum 18694 MvgAvg 623.13
###-------------------------------------------------------------Ruby
A closure:
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
A class
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
end
Run Basic
data 1,2,3,4,5,5,4,3,2,1
dim sd(10) ' series data
global sd ' make it global so we all see it
for i = 1 to 10:read sd(i): next i
x = sma(3) ' simple moving average for 3 periods
x = sma(5) ' simple moving average for 5 periods
function sma(p) ' the simple moving average function
print "----- SMA:";p;" -----"
for i = 1 to 10
sumSd = 0
for j = max((i - p) + 1,1) to i
sumSd = sumSd + sd(j) ' sum series data for the period
next j
if p > i then p1 = i else p1 = p
print sd(i);" sma:";p;" ";sumSd / p1
next i
end function----- SMA:3 ----- 1 sma:3 1 2 sma:3 1.5 3 sma:3 2 4 sma:3 3 5 sma:3 4 5 sma:3 4.6666665 4 sma:3 4.6666665 3 sma:3 4 2 sma:3 3 1 sma:3 2 ----- SMA:5 ----- 1 sma:5 1 2 sma:5 1.5 3 sma:5 2 4 sma:5 2.5 5 sma:5 3 5 sma:5 3.79999995 4 sma:5 4.1999998 3 sma:5 4.1999998 2 sma:5 3.79999995 1 sma:5 3
Rust
Vector Based
struct SimpleMovingAverage {
period: usize,
numbers: Vec<usize>
}
impl SimpleMovingAverage {
fn new(p: usize) -> SimpleMovingAverage {
SimpleMovingAverage {
period: p,
numbers: Vec::new()
}
}
fn add_number(&mut self, number: usize) -> f64 {
self.numbers.push(number);
if self.numbers.len() > self.period {
self.numbers.remove(0);
}
if self.numbers.is_empty() {
return 0f64;
}else {
let sum = self.numbers.iter().fold(0, |acc, x| acc+x);
return sum as f64 / self.numbers.len() as f64;
}
}
}
fn main() {
for period in [3, 5].iter() {
println!("Moving average with period {}", period);
let mut sma = SimpleMovingAverage::new(*period);
for i in [1, 2, 3, 4, 5, 5, 4, 3, 2, 1].iter() {
println!("Number: {} | Average: {}", i, sma.add_number(*i));
}
}
}
Double-ended Queue Based
use std::collections::VecDeque;
struct SimpleMovingAverage {
period: usize,
numbers: VecDeque<usize>
}
impl SimpleMovingAverage {
fn new(p: usize) -> SimpleMovingAverage {
SimpleMovingAverage {
period: p,
numbers: VecDeque::new()
}
}
fn add_number(&mut self, number: usize) -> f64 {
self.numbers.push_back(number);
if self.numbers.len() > self.period {
self.numbers.pop_front();
}
if self.numbers.is_empty() {
return 0f64;
}else {
let sum = self.numbers.iter().fold(0, |acc, x| acc+x);
return sum as f64 / self.numbers.len() as f64;
}
}
}
fn main() {
for period in [3, 5].iter() {
println!("Moving average with period {}", period);
let mut sma = SimpleMovingAverage::new(*period);
for i in [1, 2, 3, 4, 5, 5, 4, 3, 2, 1].iter() {
println!("Number: {} | Average: {}", i, sma.add_number(*i));
}
}
}
Moving average with period 3 Number: 1 | Average: 1 Number: 2 | Average: 1.5 Number: 3 | Average: 2 Number: 4 | Average: 3 Number: 5 | Average: 4 Number: 5 | Average: 4.666666666666667 Number: 4 | Average: 4.666666666666667 Number: 3 | Average: 4 Number: 2 | Average: 3 Number: 1 | Average: 2 Moving average with period 5 Number: 1 | Average: 1 Number: 2 | Average: 1.5 Number: 3 | Average: 2 Number: 4 | Average: 2.5 Number: 5 | Average: 3 Number: 5 | Average: 3.8 Number: 4 | Average: 4.2 Number: 3 | Average: 4.2 Number: 2 | Average: 3.8 Number: 1 | Average: 3
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
}
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
(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))
- Output:
(1 3/2 2 3 4 14/3 14/3 4 3 2)
Sidef
Implemented with closures:
func simple_moving_average(period) {
var list = []
var sum = 0
func (number) {
list.append(number)
sum += number
if (list.len > period) {
sum -= list.shift
}
(sum / list.length)
}
}
var ma3 = simple_moving_average(3)
var ma5 = simple_moving_average(5)
for num (1..5, flip(1..5)) {
printf("Next number = %d, SMA_3 = %.3f, SMA_5 = %.1f\n",
num, ma3.call(num), ma5.call(num))
}
Implemented as a class:
class sma_generator(period, list=[], sum=0) {
method SMA(number) {
list.append(number)
sum += number
if (list.len > period) {
sum -= list.shift
}
(sum / list.len)
}
}
var ma3 = sma_generator(3)
var ma5 = sma_generator(5)
for num (1..5, flip(1..5)) {
printf("Next number = %d, SMA_3 = %.3f, SMA_5 = %.1f\n",
num, ma3.SMA(num), ma5.SMA(num))
}
- Output:
Next number = 1, SMA_3 = 1.000, SMA_5 = 1.0 Next number = 2, SMA_3 = 1.500, SMA_5 = 1.5 Next number = 3, SMA_3 = 2.000, SMA_5 = 2.0 Next number = 4, SMA_3 = 3.000, SMA_5 = 2.5 Next number = 5, SMA_3 = 4.000, SMA_5 = 3.0 Next number = 5, SMA_3 = 4.667, SMA_5 = 3.8 Next number = 4, SMA_3 = 4.667, SMA_5 = 4.2 Next number = 3, SMA_3 = 4.000, SMA_5 = 4.2 Next number = 2, SMA_3 = 3.000, SMA_5 = 3.8 Next number = 1, SMA_3 = 2.000, SMA_5 = 3.0
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
]
].
|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
]
Swift
struct SimpleMovingAverage {
var period: Int
var numbers = [Double]()
mutating func addNumber(_ n: Double) -> Double {
numbers.append(n)
if numbers.count > period {
numbers.removeFirst()
}
guard !numbers.isEmpty else {
return 0
}
return numbers.reduce(0, +) / Double(numbers.count)
}
}
for period in [3, 5] {
print("Moving average with period \(period)")
var averager = SimpleMovingAverage(period: period)
for n in [1.0, 2, 3, 4, 5, 5, 4, 3, 2, 1] {
print("n: \(n); average \(averager.addNumber(n))")
}
}
- Output:
Moving average with period 3 n: 1.0; average 1.0 n: 2.0; average 1.5 n: 3.0; average 2.0 n: 4.0; average 3.0 n: 5.0; average 4.0 n: 5.0; average 4.666666666666667 n: 4.0; average 4.666666666666667 n: 3.0; average 4.0 n: 2.0; average 3.0 n: 1.0; average 2.0 Moving average with period 5 n: 1.0; average 1.0 n: 2.0; average 1.5 n: 3.0; average 2.0 n: 4.0; average 2.5 n: 5.0; average 3.0 n: 5.0; average 3.8 n: 4.0; average 4.2 n: 3.0; average 4.2 n: 2.0; average 3.8 n: 1.0; average 3.0
Tcl
or
oo::class create SimpleMovingAverage {
variable vals idx
constructor {{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])}
}
}
Demonstration:
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]"
}
- 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.
:1->C
:While 1
:Prompt I
:C->dim(L1)
:I->L1(C)
:Disp mean(L1)
:1+C->C
:EndTI-89 BASIC
Function that returns a list containing the averaged data of the supplied argument
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
EndFuncProgram that returns a simple value at each invocation:
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_
EndPrgmExample1: 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
VBA
This is a "simple" moving average.
Class sma
'to be stored in a class module with name "sma"
Private n As Integer 'period
Private arr() As Double 'circular list
Private index As Integer 'pointer into arr
Private oldsma As Double
Public Sub init(size As Integer)
n = size
ReDim arr(n - 1)
index = 0
End Sub
Public Function sma(number As Double) As Double
sma = oldsma + (-arr(index) + number) / n
oldsma = sma
arr(index) = number
index = (index + 1) Mod n
End Function
Normal module
Public Sub main()
s = [{1,2,3,4,5,5,4,3,2,1}]
Dim sma3 As New sma
Dim sma5 As New sma
sma3.init 3
sma5.init 5
For i = 1 To UBound(s)
Debug.Print i, Format(sma3.sma(CDbl(s(i))), "0.00000"),
Debug.Print Format(sma5.sma(CDbl(s(i))), "0.00000")
Next i
End Sub
- Output:
1 0,33333 0,20000 2 1,00000 0,60000 3 2,00000 1,20000 4 3,00000 2,00000 5 4,00000 3,00000 6 4,66667 3,80000 7 4,66667 4,20000 8 4,00000 4,20000 9 3,00000 3,80000 10 2,00000 3,00000
VBScript
data = "1,2,3,4,5,5,4,3,2,1"
token = Split(data,",")
stream = ""
WScript.StdOut.WriteLine "Number" & vbTab & "SMA3" & vbTab & "SMA5"
For j = LBound(token) To UBound(token)
If Len(stream) = 0 Then
stream = token(j)
Else
stream = stream & "," & token(j)
End If
WScript.StdOut.WriteLine token(j) & vbTab & Round(SMA(stream,3),2) & vbTab & Round(SMA(stream,5),2)
Next
Function SMA(s,p)
If Len(s) = 0 Then
SMA = 0
Exit Function
End If
d = Split(s,",")
sum = 0
If UBound(d) + 1 >= p Then
c = 0
For i = UBound(d) To LBound(d) Step -1
sum = sum + Int(d(i))
c = c + 1
If c = p Then
Exit For
End If
Next
SMA = sum / p
Else
For i = UBound(d) To LBound(d) Step -1
sum = sum + Int(d(i))
Next
SMA = sum / (UBound(d) + 1)
End If
End Function
- Output:
Number SMA3 SMA5 1 1 1 2 1.5 1.5 3 2 2 4 3 2.5 5 4 3 5 4.67 3.8 4 4.67 4.2 3 4 4.2 2 3 3.8 1 2 3
V (Vlang)
fn sma(period int) fn(f64) f64 {
mut i := int(0)
mut sum := f64(0)
mut storage := []f64{len: 0, cap:period}
return fn[mut storage, mut sum, mut i, period](input f64) f64 {
if storage.len < period {
sum += input
storage << input
}
sum += input - storage[i]
storage[i], i = input, (i+1)%period
return sum / f64(storage.len)
}
}
fn main() {
sma3 := sma(3)
sma5 := sma(5)
println("x sma3 sma5")
for x in [f64(1), 2, 3, 4, 5, 5, 4, 3, 2, 1] {
println("${x:5.3f} ${sma3(x):5.3f} ${sma5(x):5.3f}")
}
}- 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
Wren
import "./fmt" for Fmt
var sma = Fn.new { |period|
var i = 0
var sum = 0
var storage = []
return Fn.new { |input|
if (storage.count < period) {
sum = sum + input
storage.add(input)
}
sum = sum + input - storage[i]
storage[i] = input
i = (i+1) % period
return sum/storage.count
}
}
var sma3 = sma.call(3)
var sma5 = sma.call(5)
System.print(" x sma3 sma5")
for (x in [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) {
Fmt.precision = 3
Fmt.print("$5f $5f $5f", x, sma3.call(x), sma5.call(x))
}
- 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
zkl
fcn SMA(P){
fcn(n,ns,P){
sz:=ns.append(n.toFloat()).len();
if(P>sz) return(0.0);
if(P<sz) ns.del(0);
ns.sum(0.0)/P;
}.fp1(List.createLong(P+1),P) // pre-allocate a list of length P+1
}fp1 creates a partial application fixing the (in this case) the second and third parameters
T(1,2,3,4,5,5,4,3,2,1).apply(SMA(3)).println();
T(1,2,3,4,5,5,4,3,2,1).apply(SMA(5)).println();- Output:
L(0,0,2,3,4,4.66667,4.66667,4,3,2) L(0,0,0,0,3,3.8,4.2,4.2,3.8,3)
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