⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

When calculating the [[wp:Mean of circular quantities|average or mean of an angle]] one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.

If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.

To calculate the mean angle of several angles:

# Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.

(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)

You can alternatively use this formula:

: Given the angles $\alpha_1,\dots,\alpha_n$ the mean is computed by

::$\bar\left\{\alpha\right\} = \operatorname\left\{atan2\right\}\left\left(\frac\left\{1\right\}\left\{n\right\}\cdot\sum_\left\{j=1\right\}^n \sin\alpha_j, \frac\left\{1\right\}\left\{n\right\}\cdot\sum_\left\{j=1\right\}^n \cos\alpha_j\right\right)$

# write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.

(You should use a built-in function if you have one that does this for degrees or radians).

# Use the function to compute the means of these lists of angles (in degrees):

#* [350, 10] #* [90, 180, 270, 360] #* [10, 20, 30]

## 11l

{{trans|C#}}

F mean_angle(angles)
V x = sum(angles.map(a -> cos(radians(a)))) / angles.len
V y = sum(angles.map(a -> sin(radians(a)))) / angles.len
R degrees(atan2(y, x))

print(mean_angle([350, 10]))
print(mean_angle([90, 180, 270, 360]))
print(mean_angle([10, 20, 30]))


{{out}}


-1.61481e-15
-90
20



An implementation based on the formula using the "Arctan" (atan2) function, thus avoiding complex numbers:

with Ada.Text_IO, Ada.Numerics.Generic_Elementary_Functions;

procedure Mean_Angles is

type X_Real is digits 4;      -- or more digits for improved precision
subtype Real is X_Real range 0.0 .. 360.0; -- the range of interest
type Angles is array(Positive range <>) of Real;

procedure Put(R: Real) is
begin
IO.Put(R, Fore => 3, Aft => 2, Exp => 0);
end Put;

function Mean_Angle(A: Angles) return Real is
Sin_Sum, Cos_Sum: X_Real := 0.0; -- X_Real since sums might exceed 360.0
use Math;
begin
for I in A'Range loop
Sin_Sum := Sin_Sum + Sin(A(I), Cycle => 360.0);
Cos_Sum := Cos_Sum + Cos(A(I), Cycle => 360.0);
end loop;
return Arctan(Sin_Sum / X_Real(A'Length), Cos_Sum / X_Real(A'Length),
Cycle => 360.0);
-- may raise Ada.Numerics.Argument_Error if inputs are
-- numerically instable, e.g., when Cos_Sum is 0.0
end Mean_Angle;

begin
Put(Mean_Angle((10.0, 20.0, 30.0)));     Ada.Text_IO.New_Line;    -- 20.00
Put(Mean_Angle((90.0, 180.0, 270.0, 360.0))); -- Ada.Numerics.Argument_Error!
end Mean_Angles;


{{out}}

 20.00
0.00



## ALGOL 68

{{works with|ALGOL 68|Revision 1}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-2.8.3 algol68g-2.8.3].}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}} {{trans|C|Note: This specimen retains the original [[#C|C]] coding style}} '''File: Averages_Mean_angle.a68'''

#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #

PROC mean angle = ([]#LONG# REAL angles)#LONG# REAL:
(
INT size = UPB angles - LWB angles + 1;
#LONG# REAL y part := 0, x part := 0;
FOR i FROM LWB angles TO UPB angles DO
x part +:= #long# cos (angles[i] * #long# pi / 180);
y part +:= #long# sin (angles[i] * #long# pi / 180)
OD;

#long# arc tan2 (y part / size, x part / size) * 180 / #long# pi
);

main:
(
[]#LONG# REAL angle set 1 = ( 350, 10 );
[]#LONG# REAL angle set 2 = ( 90, 180, 270, 360);
[]#LONG# REAL angle set 3 = ( 10, 20, 30);

FORMAT summary fmt=$"Mean angle for "g" set :"-zd.ddddd" degrees"l$;
printf ((summary fmt,"1st", mean angle (angle set 1)));
printf ((summary fmt,"2nd", mean angle (angle set 2)));
printf ((summary fmt,"3rd", mean angle (angle set 3)))
)


{{out}}


Mean angle for 1st set : -0.00000 degrees
Mean angle for 2nd set :-90.00000 degrees
Mean angle for 3rd set : 20.00000 degrees



## Aime

real
mean(list l)
{
integer i;
real x, y;

x = y = 0;

i = 0;
while (i < l_length(l)) {
x += Gcos(l[i]);
y += Gsin(l[i]);
i += 1;
}

return Gatan2(y / l_length(l), x / l_length(l));
}

integer
main(void)
{
o_form("mean of 1st set: /d6/\n", mean(l_effect(350, 10)));
o_form("mean of 2nd set: /d6/\n", mean(l_effect(90, 180, 270, 360)));
o_form("mean of 3rd set: /d6/\n", mean(l_effect(10, 20, 30)));

return 0;
}


{{out}}

mean of 1st set: -.000000
mean of 2nd set: -90
mean of 3rd set: 19.999999


## AutoHotkey

{{works with|AutoHotkey 1.1}}

Angles :=  [[350, 10], [90, 180, 270, 360], [10, 20, 30]]
MsgBox, % MeanAngle(Angles[1]) "n"
. MeanAngle(Angles[2]) "n"
. MeanAngle(Angles[3])

MeanAngle(a, x=0, y=0) {
static c := ATan(1) / 45
for k, v in a {
x += Cos(v * c) / a.MaxIndex()
y += Sin(v * c) / a.MaxIndex()
}
return atan2(x, y) / c
}

atan2(x, y) {
return dllcall("msvcrt\atan2", "Double",y, "Double",x, "CDECL Double")
}


'''Output:'''

-0.000000
-90.000000
20.000000


## AWK

#!/usr/bin/awk -f
{
PI = atan2(0,-1);
x=0.0; y=0.0;
for (i=1; i<=NF; i++) {
p = $i*PI/180.0; x += sin(p); y += cos(p); } p = atan2(x,y)*180.0/PI; if (p<0) p += 360; print p; }   echo 350 10 | ./mean_angle.awk 360 echo 10 20 30 | ./mean_angle.awk 20 echo 90 180 270 360 | ./mean_angle.awk 270  ## BBC BASIC {{works with|BBC BASIC for Windows}}  *FLOAT 64 DIM angles(3) angles() = 350,10 PRINT FNmeanangle(angles(), 2) angles() = 90,180,270,360 PRINT FNmeanangle(angles(), 4) angles() = 10,20,30 PRINT FNmeanangle(angles(), 3) END DEF FNmeanangle(angles(), N%) LOCAL I%, sumsin, sumcos FOR I% = 0 TO N%-1 sumsin += SINRADangles(I%) sumcos += COSRADangles(I%) NEXT = DEGFNatan2(sumsin, sumcos) DEF FNatan2(y,x) : ON ERROR LOCAL = SGN(y)*PI/2 IF x>0 THEN = ATN(y/x) ELSE IF y>0 THEN = ATN(y/x)+PI ELSE = ATN(y/x)-PI  {{out}}  -1.61480993E-15 -90 20  ## C #include <math.h> #include <stdio.h> double meanAngle (double *angles, int size) { double y_part = 0, x_part = 0; int i; for (i = 0; i < size; i++) { x_part += cos (angles[i] * M_PI / 180); y_part += sin (angles[i] * M_PI / 180); } return atan2 (y_part / size, x_part / size) * 180 / M_PI; } int main () { double angleSet1[] = { 350, 10 }; double angleSet2[] = { 90, 180, 270, 360}; double angleSet3[] = { 10, 20, 30}; printf ("\nMean Angle for 1st set : %lf degrees", meanAngle (angleSet1, 2)); printf ("\nMean Angle for 2nd set : %lf degrees", meanAngle (angleSet2, 4)); printf ("\nMean Angle for 3rd set : %lf degrees\n", meanAngle (angleSet3, 3)); return 0; }  {{out}} Mean Angle for 1st set : -0.000000 degrees Mean Angle for 2nd set : -90.000000 degrees Mean Angle for 3rd set : 20.000000 degrees  ## C++ {{trans|C#}} #include <iomanip> #include <iostream> #include <vector> #define _USE_MATH_DEFINES #include <math.h> template<typename C> double meanAngle(const C& c) { auto it = std::cbegin(c); auto end = std::cend(c); double x = 0.0; double y = 0.0; double len = 0.0; while (it != end) { x += cos(*it * M_PI / 180); y += sin(*it * M_PI / 180); len++; it = std::next(it); } return atan2(y, x) * 180 / M_PI; } void printMean(std::initializer_list<double> init) { std::cout << std::fixed << std::setprecision(3) << meanAngle(init) << '\n'; } int main() { printMean({ 350, 10 }); printMean({ 90, 180, 270, 360 }); printMean({ 10, 20, 30 }); return 0; }  {{out}} -0.000 -90.000 20.000  ## C# using System; using System.Linq; using static System.Math; class Program { static double MeanAngle(double[] angles) { var x = angles.Sum(a => Cos(a * PI / 180)) / angles.Length; var y = angles.Sum(a => Sin(a * PI / 180)) / angles.Length; return Atan2(y, x) * 180 / PI; } static void Main() { Action<double[]> printMean = x => Console.WriteLine("{0:0.###}", MeanAngle(x)); printMean(new double[] { 350, 10 }); printMean(new double[] { 90, 180, 270, 360 }); printMean(new double[] { 10, 20, 30 }); } }  {{out}} 0 -90 20  ## Clojure (defn mean-fn [k coll] (let [n (count coll) trig (get {:sin #(Math/sin %) :cos #(Math/cos %)} k)] (* (/ 1 n) (reduce + (map trig coll))))) (defn mean-angle [degrees] (let [radians (map #(Math/toRadians %) degrees) a (mean-fn :sin radians) b (mean-fn :cos radians)] (Math/toDegrees (Math/atan2 a b))))  Example: (mean-angle [350 10]) ;=> -1.614809932057922E-15 (mean-angle [90 180 270 360]) ;=> -90.0 (mean-angle [10 20 30]) ;=> 19.999999999999996  ## Common Lisp (defun average (list) (/ (reduce #'+ list) (length list))) (defun radians (angle) (* pi 1/180 angle)) (defun degrees (angle) (* 180 (/ 1 pi) angle)) (defun mean-angle (angles) (let* ((angles (map 'list #'radians angles)) (cosines (map 'list #'cos angles)) (sines (map 'list #'sin angles))) (degrees (atan (average sines) (average cosines))))) (loop for angles in '((350 10) (90 180 270 360) (10 20 30)) do (format t "~&The mean angle of ~a is ~$°." angles (mean-angle angles)))


{{out}}

The mean angle of (350 10) is -0.00°.
The mean angle of (90 180 270 360) is -90.00°.
The mean angle of (10 20 30) is 20.00°.


## D

import std.stdio, std.algorithm, std.complex;
import std.math: PI;

auto radians(T)(in T d) pure nothrow @nogc { return d * PI / 180; }
auto degrees(T)(in T r) pure nothrow @nogc { return r * 180 / PI; }

real meanAngle(T)(in T[] D) pure nothrow @nogc {
immutable t = reduce!((a, d) => a + d.radians.expi)(0.complex, D);
return (t / D.length).arg.degrees;
}

void main() {
foreach (angles; [[350, 10], [90, 180, 270, 360], [10, 20, 30]])
writefln("The mean angle of %s is: %.2f degrees",
angles, angles.meanAngle);
}


{{out}}

The mean angle of [350, 10] is: -0.00 degrees
The mean angle of [90, 180, 270, 360] is: 90.00 degrees
The mean angle of [10, 20, 30] is: 20.00 degrees


## EchoLisp


(define-syntax-rule  (deg->radian deg) (* deg 1/180 PI))

(define (mean-angles angles)
(angle
(for/sum ((a angles)) (make-polar 1 (deg->radian a))))))

(mean-angles '( 350 10))
→ -0
(mean-angles '[90 180 270 360])
→ -90
(mean-angles '[10 20 30])
→ 20



## Elixir


defmodule MeanAngle do
def mean_angle(angles) do
sines = rad_angles |> Enum.map(&:math.sin/1) |> Enum.sum
cosines = rad_angles |> Enum.map(&:math.cos/1) |> Enum.sum

end

(:math.pi/180) * a
end

(180/:math.pi) * a
end
end

IO.inspect MeanAngle.mean_angle([10, 350])
IO.inspect MeanAngle.mean_angle([90, 180, 270, 360])
IO.inspect MeanAngle.mean_angle([10, 20, 30])



{{out}}


-1.614809932057922e-15
-90.0
19.999999999999996



## Erlang

The function from_degrees/1 is used to solve [[Averages/Mean_time_of_day]]. Please keep backwards compatibility when editing. Or update the other module, too.


-module( mean_angle ).

from_degrees( Angles ) ->
Sines = [math:sin(X) || X <- Radians],
Coses = [math:cos(X) || X <- Radians],
degrees( math:atan2( average(Sines), average(Coses) ) ).

Angles = [[350, 10], [90, 180, 270, 360], [10, 20, 30]],
[io:fwrite( "Mean angle of ~p is: ~p~n", [X, erlang:round(from_degrees(X))] ) || X <- Angles].

average( List ) -> lists:sum( List ) / erlang:length( List ).

radians( Degrees ) -> Degrees * math:pi() / 180.



{{out}}


Mean angle of [350,10] is: 0
Mean angle of [90,180,270,360] is: -90
Mean angle of [10,20,30] is: 20



## Euler Math Toolbox

function meanangle (a) ...
$z=sum(exp(rad(a)*I));$  if z~=0 then error("Not meaningful");
$else return deg(arg(z))$  endfunction
>meanangle([350,10])
0
>meanangle([90,180,270,360])
Error : Not meaningful

Error generated by error() command

Error in function meanangle in line
if z~=0 then error("Not meaningful");
>meanangle([10,20,30])
20


## Euphoria

{{works with|OpenEuphoria}}


include std/console.e
include std/mathcons.e

sequence AngleList = {{350,10},{90,180,270,360},{10,20,30}}

function atan2(atom y, atom x)
return 2*arctan((sqrt(power(x,2)+power(y,2)) - x)/y)
end function

function MeanAngle(sequence angles)
atom x = 0, y = 0
integer l = length(angles)

for i = 1 to length(angles) do
x += cos(angles[i] * PI / 180)
y += sin(angles[i] * PI / 180)
end for

return atan2(y / l, x / l) * 180 / PI
end function

for i = 1 to length(AngleList) do
printf(1,"Mean Angle for set %d:  %3.5f\n",{i,MeanAngle(AngleList[i])})
end for

if getc(0) then end if



{{out}}


Mean Angle for set 1:  0.00000
Mean Angle for set 2:  -90.00000
Mean Angle for set 3:  20.00000



open System
open System.Numerics

let deg2rad d = d * Math.PI / 180.
let rad2deg r = r * 180. / Math.PI

[<EntryPoint>]
let main argv =
let makeComplex = fun r ->  Complex.FromPolarCoordinates(1., r)
argv
|> Seq.map (Double.Parse >> deg2rad >> makeComplex)
|> Seq.fold (fun x y -> Complex.Add(x,y)) Complex.Zero
|> fun c -> c.Phase |> rad2deg
|> printfn "Mean angle for [%s]: %g°" (String.Join("; ",argv))
0


{{out}}

>RosettaCode 350 10
Mean angle for [350; 10]: -2.74518e-14°

>RosettaCode 10 20 30
Mean angle for [10; 20; 30]: 20°

>RosettaCode 90 180 270 360
Mean angle for [90; 180; 270; 360]: -90°



## Factor

USING: formatting kernel math math.functions math.libm math.trig
sequences ;

: mean-angle ( seq -- x )
[ deg>rad ] map [ [ sin ] map-sum ] [ [ cos ] map-sum ]
[ length ] tri recip [ * ] curry bi@ fatan2 rad>deg ;

: show ( seq -- )
dup mean-angle "The mean angle of %u is: %f°\n" printf ;

{ { 350 10 } { 90 180 270 360 } { 10 20 30 } } [ show ] each


{{out}}


The mean angle of { 350 10 } is: -0.000000°
The mean angle of { 90 180 270 360 } is: -90.000000°
The mean angle of { 10 20 30 } is: 20.000000°



## Fortran

Please find the example output along with the build instructions in the comments at the start of the FORTRAN 2008 source. Compiler: gfortran from the GNU compiler collection. Command interpreter: bash.


!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Mon Jun  3 18:07:59
!
!a=./f && make $a && OMP_NUM_THREADS=2$a
!gfortran -std=f2008 -Wall -fopenmp -ffree-form -fall-intrinsics -fimplicit-none f.f08 -o f
!  -7.80250048E-06         350          10
!   90.0000000              90         180         270         360
!   19.9999962              10          20          30
!
!Compilation finished at Mon Jun  3 18:07:59

program average_angles
!real(kind=8), parameter :: TAU = 6.283185307179586232 ! http://tauday.com/
!integer, dimension(13), parameter :: test_data = (/2,350,10, 4,90,180,270,360, 3,10,20,30, 0/)
!integer :: i, j, n
!complex(kind=16) :: some
!real(kind=8) :: angle
real, parameter :: TAU = 6.283185307179586232 ! http://tauday.com/
integer, dimension(13), parameter :: test_data = (/2,350,10, 4,90,180,270,360, 3,10,20,30, 0/)
integer :: i, j, n
complex :: some
real :: angle
i = 1
n = int(test_data(i))
do while (0 .lt. n)
some = 0
do j = 1, n
angle = (TAU/360)*test_data(i+j)
some = some + cmplx(cos(angle), sin(angle))
end do
some = some / n
write(6,*)(360/TAU)*atan2(aimag(some), real(some)),test_data(i+1:i+n)
i = i + n + 1
n = int(test_data(i))
end do
end program average_angles



## FreeBASIC


' FB 1.05.0 Win64

Const PI As Double = 3.1415926535897932

Function MeanAngle(angles() As Double) As Double
Dim As Integer length = Ubound(angles) - Lbound(angles) + 1
Dim As Double sinSum = 0.0
Dim As Double cosSum = 0.0
For i As Integer = LBound(angles) To UBound(angles)
sinSum += Sin(angles(i) * PI / 180.0)
cosSum += Cos(angles(i) * PI / 180.0)
Next
Return Atan2(sinSum / length, cosSum / length) * 180.0 / PI
End Function

Dim As Double angles1(1 To 2) = {350, 10}
Dim As Double angles2(1 To 4) = {90, 180, 270, 360}
Dim As Double angles3(1 To 3) = {10, 20, 30}

Print Using "Mean for angles 1 is : ####.## degrees"; MeanAngle(angles1())
Print Using "Mean for angles 2 is : ####.## degrees"; MeanAngle(angles2())
Print Using "Mean for angles 3 is : ####.## degrees"; MeanAngle(angles3())
Print
Print "Press any key to quit the program"
Sleep



{{out}}


Mean for angles 1 is :   -0.00 degrees
Mean for angles 2 is :  -90.00 degrees
Mean for angles 3 is :   20.00 degrees



## Go

### Complex

package main

import (
"fmt"
"math"
"math/cmplx"
)

func deg2rad(d float64) float64 { return d * math.Pi / 180 }
func rad2deg(r float64) float64 { return r * 180 / math.Pi }

func mean_angle(deg []float64) float64 {
sum := 0i
for _, x := range deg {
}
}

func main() {
for _, angles := range [][]float64{
{350, 10},
{90, 180, 270, 360},
{10, 20, 30},
} {
fmt.Printf("The mean angle of %v is: %f degrees\n", angles, mean_angle(angles))
}
}


{{out}}


The mean angle of [350 10] is: -0.000000 degrees
The mean angle of [90 180 270 360] is: -90.000000 degrees
The mean angle of [10 20 30] is: 20.000000 degrees



### Atan2

A mean_angle function that could be substituted above. Functions deg2rad and rad2deg are not used here but there is no runtime advantage either way to using them or not. Inlining should result in eqivalent code being generated. Also the Go Atan2 library function has no limits on the arguments so there is no need to divide by the number of elements.

func mean_angle(deg []float64) float64 {
var ss, sc float64
for _, x := range deg {
s, c := math.Sincos(x * math.Pi / 180)
ss += s
sc += c
}
return math.Atan2(ss, sc) * 180 / math.Pi
}


## Groovy

import static java.lang.Math.*
def meanAngle = {
atan2( it.sum { sin(it * PI / 180) } / it.size(), it.sum { cos(it * PI / 180) } / it.size()) * 180 / PI
}


Test:

def verifyAngle = { angles ->
def ma = meanAngle(angles)
printf("Mean Angle for $angles: %5.2f%n", ma) round(ma * 100) / 100.0 } assert verifyAngle([350, 10]) == -0 assert verifyAngle([90, 180, 270, 360]) == -90 assert verifyAngle([10, 20, 30]) == 20  {{out}} Mean Angle for [350, 10]: -0.00 Mean Angle for [90, 180, 270, 360]: -90.00 Mean Angle for [10, 20, 30]: 20.00  ## Haskell import Data.Complex (cis, phase) meanAngle :: RealFloat c => [c] -> c meanAngle = (/ pi) . (* 180) . phase . sum . map (cis . (/ 180) . (* pi)) main :: IO () main = mapM_ (\angles -> putStrLn$
"The mean angle of " ++
show angles ++ " is: " ++ show (meanAngle angles) ++ " degrees")
[[350, 10], [90, 180, 270, 360], [10, 20, 30]]


{{out}}


The mean angle of [350.0,10.0] is: -2.745176884498468e-14 degrees
The mean angle of [90.0,180.0,270.0,360.0] is: -90.0 degrees
The mean angle of [10.0,20.0,30.0] is: 19.999999999999996 degrees



Alternative Solution: This solution gives an insight about using factoring, many small functions like Forth and using function composition.



-- file: trigdeg.fs

atan2d y x = rad2deg (atan2 y x )

avg_angle angles = atan2d y x
where
y = mean (map sind angles)
x = mean (map cosd angles)

-- End of trigdeg.fs --------



{{out}}



-- GHCI shell  $ghci Prelude> :load trigdeg.hs [1 of 1] Compiling Main ( trigdeg.hs, interpreted ) Ok, modules loaded: Main. *Main> *Main> avg_angle [350.0, 10.0] -2.745176884498468e-14 *Main> *Main> avg_angle [90.0, 180.0, 270.0, 360.0 ] -90.0 *Main> mean [10.0, 20.0, 30.0] 20.0 *Main>  =={{header|Icon}} and {{header|Unicon}}== procedure main(A) write("Mean angle is ",meanAngle(A)) end procedure meanAngle(A) every (sumSines := 0.0) +:= sin(dtor(!A)) every (sumCosines := 0.0) +:= cos(dtor(!A)) return rtod(atan(sumSines/*A,sumCosines/*A)) end  Sample runs:  ->ama 10 350 Mean angle is -2.745176884498468e-14 ->ama 90 180 270 360 Mean angle is -90.0 ->ama 10 20 30 Mean angle is 20.0  ## J avgAngleD=: 360|(_1 { [: (**|)&.+.@(+/ % #)&.(*.inv) 1,.])&.(1r180p1&*)  This verb can be represented as simpler component verbs, for example: rfd=: 1r180p1&* NB. convert angle to radians from degrees toComplex=: *.inv NB. maps integer pairs as length, complex angle (in radians) mean=: +/ % # NB. calculate arithmetic mean roundComplex=: (* * |)&.+. NB. discard an extraneous least significant bit of precision from a complex value whose magnitude is in the vicinity of 1 avgAngleR=: _1 { [: roundComplex@mean&.toComplex 1 ,. ] NB. calculate average angle in radians avgAngleD=: 360|avgAngleR&.rfd NB. calculate average angle in degrees  Example use:  avgAngleD 10 350 0 avgAngleD 90 180 270 360 NB. result not meaningful 0 avgAngleD 10 20 30 20 avgAngleD 20 350 5 avgAngleD 10 340 355  Notes: (**|)&.+. is an expression to discard an extraneous least significant bit of precision from a complex value whose magnitude is in the vicinity of 1. (+/ % #) finds the (Pythagorean) mean verb&.(*.inv) maps integer pairs as length,complex angle (in radians) and uses the verb in the domain of complex numbers, and then maps the result back to length,angle. (1,.]) prefixes every value in a list with 1 (forming a two column table) (_1 { verb) takes the last item from the result of the verb (and note that after we average our complex values and convert them back to length/angle format, we will be working with a list of two elements: length and angle -- and we do not care about length, which will usually be less than 1). verb&.(1r180p1&*) converts its argument from degrees to radians, uses the verb in the radian domain, then converts the result of that argument back to degrees. 360|verb ensures that the result is not negative and is also less than 360 ## Java {{trans|NetRexx}} {{works with|Java|7+}} import java.util.Arrays; public class AverageMeanAngle { public static void main(String[] args) { printAverageAngle(350.0, 10.0); printAverageAngle(90.0, 180.0, 270.0, 360.0); printAverageAngle(10.0, 20.0, 30.0); printAverageAngle(370.0); printAverageAngle(180.0); } private static void printAverageAngle(double... sample) { double meanAngle = getMeanAngle(sample); System.out.printf("The mean angle of %s is %s%n", Arrays.toString(sample), meanAngle); } public static double getMeanAngle(double... anglesDeg) { double x = 0.0; double y = 0.0; for (double angleD : anglesDeg) { double angleR = Math.toRadians(angleD); x += Math.cos(angleR); y += Math.sin(angleR); } double avgR = Math.atan2(y / anglesDeg.length, x / anglesDeg.length); return Math.toDegrees(avgR); } }  {{out}} The mean angle of [350.0, 10.0] is -1.614809932057922E-15 The mean angle of [90.0, 180.0, 270.0, 360.0] is -90.0 The mean angle of [10.0, 20.0, 30.0] is 19.999999999999996 The mean angle of [370.0] is 9.999999999999977 The mean angle of [180.0] is 180.0  ## JavaScript ### atan2 function sum(a) { var s = 0; for (var i = 0; i < a.length; i++) s += a[i]; return s; } function degToRad(a) { return Math.PI / 180 * a; } function meanAngleDeg(a) { return 180 / Math.PI * Math.atan2( sum(a.map(degToRad).map(Math.sin)) / a.length, sum(a.map(degToRad).map(Math.cos)) / a.length ); } var a = [350, 10], b = [90, 180, 270, 360], c = [10, 20, 30]; console.log(meanAngleDeg(a)); console.log(meanAngleDeg(b)); console.log(meanAngleDeg(c));  {{out}} -1.614809932057922e-15 -90 19.999999999999996  ## jq {{works with|jq|1.4}} To avoid anomalies, the following is designed to assign the null value as the mean angle in cases such as [0, 180]. '''Generic Infrastructure''' def pi: 4 * (1|atan); def deg2rad: . * pi / 180; def rad2deg: if . == null then null else . * 180 / pi end; # Input: [x,y] (special handling of x==0) # Output: [r, theta] where theta may be null def to_polar: if .[0] == 0 then [1, if .[1] > 5e-14 then pi/2 elif .[1] < -5e-14 then -pi/2 else null end] else [1, ((.[1]/.[0]) | atan)] end; def from_polar: .[1] | [ cos, sin]; def abs: if . < 0 then - . else . end; def summation(f): map(f) | add;  '''Mean Angle''' # input: degrees def mean_angle: def round: if . == null then null elif . < 0 then -1 * ((- .) | round) | if . == -0 then 0 else . end else ((. + 3e-14) | floor) as$x
| if ($x - .) | abs < 3e-14 then$x else . end
end;

| [ summation(.[0]), summation(.[1]) ]
| to_polar
| .[1]
| round;


'''Examples'''

([350, 10], [90, 180, 270, 360], [10, 20, 30])
| "The mean angle of $$.) is: \(mean_angle)"  {{out}} jq -r -n -f Mean_angle.jq The mean angle of [350,10] is: 0 The mean angle of [90,180,270,360] is: null The mean angle of [10,20,30] is: 20  ## Julia Julia has built-in functions sind and cosd to compute the sine and cosine of angles specified in degrees accurately (avoiding the roundoff errors incurred in conversion to radians), and a built-in function to convert radians to degrees (or vice versa). Using these: using Statistics meandegrees(degrees) = radians2degrees(atan2(mean(sind(degrees)), mean(cosd(degrees))))  The output is:  meandegrees([350, 10]) 0.0 julia> meandegrees([90, 180, 270, 360]]) 0.0 julia> meandegrees([10, 20, 30]]) 19.999999999999996  (Note that the mean of 90°, 180°, 270°, and 360° gives zero because of the lack of roundoff errors in the sind function, since the standard-library atan2(0,0) value is zero. Many of the other languages report an average of 90° or –90° in this case due to rounding errors.) ## Kotlin // version 1.0.5-2 fun meanAngle(angles: DoubleArray): Double { val sinSum = angles.sumByDouble { Math.sin(it * Math.PI / 180.0) } val cosSum = angles.sumByDouble { Math.cos(it * Math.PI / 180.0) } return Math.atan2(sinSum / angles.size, cosSum / angles.size) * 180.0 / Math.PI } fun main(args: Array<String>) { val angles1 = doubleArrayOf(350.0, 10.0) val angles2 = doubleArrayOf(90.0, 180.0, 270.0, 360.0) val angles3 = doubleArrayOf(10.0, 20.0, 30.0) val fmt = "%.2f degrees" // format results to 2 decimal places println("Mean for angles 1 is {fmt.format(meanAngle(angles1))}") println("Mean for angles 2 is {fmt.format(meanAngle(angles2))}") println("Mean for angles 3 is {fmt.format(meanAngle(angles3))}") }  {{out}}  Mean for angles 1 is -0.00 degrees Mean for angles 2 is -90.00 degrees Mean for angles 3 is 20.00 degrees  ## Liberty BASIC global Pi Pi =3.1415926535 print "Mean Angle( "; chr( 34); "350,10"; chr( 34); ") = "; using( "###.#", meanAngle( "350,10")); " degrees." ' 0 print "Mean Angle( "; chr( 34); "90,180,270,360"; chr( 34); ") = "; using( "###.#", meanAngle( "90,180,270,360")); " degrees." ' -90 print "Mean Angle( "; chr( 34); "10,20,30"; chr( 34); ") = "; using( "###.#", meanAngle( "10,20,30")); " degrees." ' 20 end function meanAngle( angles) term =1 while word( angles, term, ",") <>"" angle =val( word( angles, term, ",")) sumSin = sumSin +sin( degRad( angle)) sumCos = sumCos +cos( degRad( angle)) term =term +1 wend meanAngle= radDeg( atan2( sumSin, sumCos)) if abs( sumSin) +abs( sumCos) <0.001 then notice "Not Available." +_ chr( 13) +"(" +angles +")" +_ chr( 13) +"Result nearly equals zero vector." +_ chr( 13) +"Displaying '666'.": meanAngle =666 end function function degRad( theta) degRad =theta *Pi /180 end function function radDeg( theta) radDeg =theta *180 /Pi end function function atan2( y, x) if x >0 then at =atn( y /x) if y >=0 and x <0 then at =atn( y /x) +pi if y <0 and x <0 then at =atn( y /x) -pi if y >0 and x =0 then at = pi /2 if y <0 and x =0 then at = 0 -pi /2 if y =0 and x =0 then notice "undefined": end atan2 =at end function  {{out}}  Mean Angle( "350,10") = 0.0 degrees. Mean Angle( "90,180,270,360") = 666.0 degrees. Mean Angle( "10,20,30") = 20.0 degrees.  to mean_angle :angles local "avgsin make "avgsin quotient apply "sum map "sin :angles count :angles local "avgcos make "avgcos quotient apply "sum map "cos :angles count :angles output (arctan :avgcos :avgsin) end foreach [[350 10] [90 180 270 360] [10 20 30]] [ print (sentence [The average of \(] ? [$$ is] (mean_angle ?))
]

bye



{{Out}}

The average of ( 350 10 ) is 0
The average of ( 90 180 270 360 ) is 0
The average of ( 10 20 30 ) is 20


## Lua

{{trans|Tcl}} {{works with|Lua|5.1}}

function meanAngle (angleList)
local sumSin, sumCos = 0, 0
for i, angle in pairs(angleList) do
end
local result = math.deg(math.atan2(sumSin, sumCos))
return string.format("%.2f", result)
end

print(meanAngle({350, 10}))
print(meanAngle({90, 180, 270, 360}))
print(meanAngle({10, 20, 30}))


{{out}}


-0.00
-90.00
20.00



## Maple

The following procedure takes a list of numeric degrees (with attached units) such as

 [ 350, 10 ] *~ Unit(arcdeg);
[350 [arcdeg], 10 [arcdeg]]


as input. (We could use "degree" instead of "arcdeg", since "degree" is taken, by default, to mean angle measure, but it seems best to avoid the ambiguity.)

MeanAngle := proc( L )
uses Units:-Standard; # for unit-awareness
local   u;
evalf( convert( argument( add( u, u = exp~( I *~ L ) ) ), 'units', 'radian', 'degree' ) )
end proc:


Applying this to the given data sets, we obtain:

 MeanAngle( [ 350, 10 ] *~ Unit(arcdeg) );
0.

> MeanAngle( [ 90, 180, 270, 360 ] *~ Unit(arcdeg) );
0.

> MeanAngle( [ 10, 20, 30 ] *~ Unit(arcdeg) );
20.00000000


meanAngle[data_List] := N@Arg[Mean[Exp[I data Degree]]]/Degree


{{out}}

meanAngle /@ {{350, 10}, {90, 180, 270, 360}, {10, 20, 30}}
{0., Interval[{-180., 180.}], 20.}


function u = mean_angle(phi)
u = angle(mean(exp(i*pi*phi/180)))*180/pi;
end

 mean_angle([350, 10])
ans = -2.7452e-14
mean_angle([90, 180, 270, 360])
ans = -90
mean_angle([10, 20, 30])
ans =  20.000



## NetRexx

{{trans|C}}

/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 80

runSample(arg)
return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getMeanAngle(angles) private static binary
x_component = double 0.0
y_component = double 0.0
aK = int angles.words()
loop a_ = 1 to aK
angle_d = double angles.word(a_)
x_component = x_component + Math.cos(angle_r)
y_component = y_component + Math.sin(angle_r)
end a_
x_component = x_component / aK
y_component = y_component / aK
avg_r = Math.atan2(y_component, x_component)
avg_d = Math.toDegrees(avg_r)
return avg_d

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
angleSet = [ '350 10', '90 180 270 360', '10 20 30', '370', '180' ]
loop angles over angleSet
say 'The mean angle of' angles.space(1, ',') 'is:'
say '  'getMeanAngle(angles).format(6, 6)
say
end angles
return



{{out}}


The mean angle of 350,10 is:
0.000000

The mean angle of 90,180,270,360 is:
-90.000000

The mean angle of 10,20,30 is:
20.000000

The mean angle of 370 is:
10.000000

The mean angle of 180 is:
180.000000



## Nim

import math, complex

proc rect(r, phi: float): Complex = (r * cos(phi), sin(phi))
proc phase(c: Complex): float = arctan2(c.im, c.re)

proc radians(x: float): float = (x * Pi) / 180.0
proc degrees(x: float): float = (x * 180.0) / Pi

proc meanAngle(deg: openArray[float]): float =
var c: Complex
for d in deg:
degrees(phase(c / float(deg.len)))

echo "The 1st mean angle is: ", meanAngle([350.0, 10.0]), " degrees"
echo "The 2nd mean angle is: ", meanAngle([90.0, 180.0, 270.0, 360.0]), " degrees"
echo "The 3rd mean angle is: ", meanAngle([10.0, 20.0, 30.0]), " degrees"


Output:

The 1st mean angle is: -2.745176884498468e-14 degrees
The 2nd mean angle is: -90.0 degrees
The 3rd mean angle is: 20.0 degrees



MODULE MeanAngle;
IMPORT
M := LRealMath,
Out;
CONST
toDegs = 180 / M.pi;
VAR

PROCEDURE Mean(g: ARRAY OF LONGREAL): LONGREAL;
VAR
i: INTEGER;
sumSin, sumCos: LONGREAL;
BEGIN
i := 0;sumSin := 0.0;sumCos := 0.0;
WHILE g[i] # 0.0 DO
sumSin := sumSin + M.sin(g[i] * toRads);
sumCos := sumCos + M.cos(g[i] * toRads);
INC(i)
END;
RETURN M.arctan2(sumSin / i,sumCos / i);
END Mean;

BEGIN
END MeanAngle.



{{out}}


-0.000000000
-90.000000000
20.000000000



## OCaml

let pi = 3.14159_26535_89793_23846_2643

d *. pi /. 180.0

r *. 180.0 /. pi

let mean_angle angles =
let sum_sin = List.fold_left (fun sum a -> sum +. sin a) 0.0 rad_angles
and sum_cos = List.fold_left (fun sum a -> sum +. cos a) 0.0 rad_angles
in

let test angles =
Printf.printf "The mean angle of [%s] is: %g degrees\n"
(String.concat "; " (List.map (Printf.sprintf "%g") angles))
(mean_angle angles)

let () =
test [350.0; 10.0];
test [90.0; 180.0; 270.0; 360.0];
test [10.0; 20.0; 30.0];
;;


or using the Complex module:

open Complex

let mean_angle angles =
let sum =
List.fold_left (fun sum a -> add sum (polar 1.0 (deg2rad a))) zero angles
in


{{out}}


The mean angle of [350; 10] is: -2.74518e-14 degrees
The mean angle of [90; 180; 270; 360] is: -90 degrees
The mean angle of [10; 20; 30] is: 20 degrees



## ooRexx

{{trans|REXX}}

/*REXX program computes the  mean angle  (angles expressed in degrees). */
numeric digits 50                      /*use fifty digits of precision, */
showDig=10                      /*··· but only display 10 digits.*/
xl = 350 10            ;      say showit(xl, meanAngleD(xl) )
xl = 90 180 270 360    ;      say showit(xl, meanAngleD(xl) )
xl = 10 20 30          ;      say showit(xl, meanAngleD(xl) )
exit                                   /*stick a fork in it, we're done.*/
/*----------------------------------MEANANGD subroutine-----------------*/
meanAngleD:  procedure;  parse arg xl;   numeric digits digits()+digits()%4
sum.=0
n=words(xl)
do j=1 to n
sum.0sin+=rxCalcSin(word(xl,j))
sum.0cos+=rxCalcCos(word(xl,j))
End
If sum.0cos=0 Then
Return sign(sum.0sin/n)*90
Else
Return rxCalcArcTan((sum.0sin/n)/(sum.0cos/n))

showit: procedure expose showDig;  numeric digits showDig;  parse arg a,mA
return left('angles='a,30)  'mean angle='  format(mA,,showDig,0)/1

::requires rxMath library;


{{out}}

angles=350 10                  mean angle= 0
angles=90 180 270 360          mean angle= 0
angles=10 20 30                mean angle= 20


## PARI/GP

meanAngle(v)=atan(sum(i=1,#v,sin(v[i]))/sum(i=1,#v,cos(v[i])))%(2*Pi)
meanDegrees(v)=meanAngle(v*Pi/180)*180/Pi
apply(meanDegrees,[[350, 10], [90, 180, 270, 360], [10, 20, 30]])


{{out}}

[360.000000, 296.565051, 20.0000000]


## Pascal

uses library math for sincos, a function of FPU80x87, atan2 and DegToRad. Tested with free pascal. Try to catch very small cos values and set to 0.0 degrees " Error : Not meaningful" as http://rosettacode.org/wiki/Averages/Mean_angle#Euler_Math_Toolbox complains.

program MeanAngle;
{$IFDEF DELPHI} {$APPTYPE CONSOLE}
{$ENDIF} uses math;// sincos and atan2 type tAngles = array of double; function MeanAngle(const a:tAngles;cnt:longInt):double; // calculates mean angle. // returns 0.0 if direction is not sure. const eps = 1e-10; var i : LongInt; s,c, Sumsin,SumCos : extended; begin IF cnt = 0 then Begin MeanAngle := 0.0; EXIT; end; SumSin:= 0; SumCos:= 0; For i := Cnt-1 downto 0 do Begin sincos(DegToRad(a[i]),s,c); Sumsin := sumSin+s; SumCos := sumCos+c; end; s := SumSin/cnt; c := sumCos/cnt; IF c > eps then MeanAngle := RadToDeg(arctan2(s,c)) else // Not meaningful MeanAngle := 0.0; end; Procedure OutMeanAngle(const a:tAngles;cnt:longInt); var i : longInt; Begin IF cnt > 0 then Begin write('The mean angle of ['); For i := 0 to Cnt-2 do write(a[i]:0:2,','); write(a[Cnt-1]:0:2,'] => '); writeln(MeanAngle(a,cnt):0:16); end; end; var a:tAngles; Begin setlength(a,4); a[0] := 350;a[1] := 10; OutMeanAngle(a,2); a[0] := 90;a[1] := 180;a[2] := 270;a[3] := 360; OutMeanAngle(a,4); a[0] := 10;a[1] := 20;a[2] := 30; OutMeanAngle(a,3); setlength(a,0); end.  ;output:  The mean angle of [350.00,10.00] => 0.0000000000000000 The mean angle of [90.00,180.00,270.00,360.00] => 0.0000000000000000 The mean angle of [10.00,20.00,30.00] => 20.0000000000000000  ## Perl sub Pi () { 3.1415926535897932384626433832795028842 } sub meanangle { my($x, $y) = (0,0); ($x,$y) = ($x + sin($_),$y + cos($_)) for @_; my$atan = atan2($x,$y);
$atan += 2*Pi while$atan < 0;    # Ghetto fmod
$atan -= 2*Pi while$atan > 2*Pi;
$atan; } sub meandegrees { meanangle( map {$_ * Pi/180 } @_ ) * 180/Pi;
}

print "The mean angle of [@$_] is: ", meandegrees(@$_), " degrees\n"
for ([350,10], [90,180,270,360], [10,20,30]);


{{out}}


The mean angle of [350 10] is: 360 degrees
The mean angle of [90 180 270 360] is: 270 degrees
The mean angle of [10 20 30] is: 20 degrees



## Perl 6

{{works with|Rakudo|2015.12}} This solution refuses to return an answer when the angles cancel out to a tiny magnitude.

# Of course, you can still use pi and 180.
sub deg2rad { $^d * tau / 360 } sub rad2deg {$^r * 360 / tau }

sub phase ($c) { my ($mag,$ang) =$c.polar;
return NaN if $mag < 1e-16;$ang;
}

sub meanAngle { rad2deg phase [+] map { cis deg2rad $_ }, @^angles } say meanAngle($_).fmt("%.2f\tis the mean angle of "), $_ for [350, 10], [90, 180, 270, 360], [10, 20, 30];  {{out}} -0.00 is the mean angle of 350 10 NaN is the mean angle of 90 180 270 360 20.00 is the mean angle of 10 20 30  ## Phix Copied from [[Euphoria]], and slightly improved function atan2(atom y, atom x) return 2*arctan((sqrt(power(x,2)+power(y,2))-x)/y) end function function MeanAngle(sequence angles) atom x=0, y=0, ai_rad integer l=length(angles) for i=1 to l do ai_rad = angles[i]*PI/180 x += cos(ai_rad) y += sin(ai_rad) end for if abs(x)<1e-16 then return "not meaningful" end if return sprintf("%9.5f",atan2(y,x)*180/PI) end function constant AngleLists = {{350,10},{90,180,270,360},{10,20,30},{180},{0,180}} sequence ai for i=1 to length(AngleLists) do ai = AngleLists[i] printf(1,"%+16s: Mean Angle is %s\n",{sprint(ai),MeanAngle(ai)}) end for {} = wait_key()  {{out}}  {350,10}: Mean Angle is 0.00000 {90,180,270,360}: Mean Angle is not meaningful {10,20,30}: Mean Angle is 20.00000 {180}: Mean Angle is 180.00000 {0,180}: Mean Angle is not meaningful  ## PHP {{trans|C}} <?php$samples = array(
'1st' => array(350, 10),
'2nd' => array(90, 180, 270, 360),
'3rd' => array(10, 20, 30)
);

foreach($samples as$key => $sample){ echo 'Mean angle for ' .$key . ' sample: ' . meanAngle($sample) . ' degrees.' . PHP_EOL; } function meanAngle ($angles){
$y_part =$x_part = 0;
$size = count($angles);
for ($i = 0;$i < $size;$i++){
$x_part += cos(deg2rad($angles[$i]));$y_part += sin(deg2rad($angles[$i]));
}
$x_part /=$size;
$y_part /=$size;
return rad2deg(atan2($y_part,$x_part));
}
?>


{{out}}

Mean angle for 1st sample: -1.6148099320579E-15 degrees.
Mean angle for 2nd sample: -90 degrees.
Mean angle for 3rd sample: 20 degrees.


## PicoLisp

(load "@lib/math.l")

(de meanAngle (Lst)
(*/
(atan2
(sum '((A) (sin (*/ A pi 180.0))) Lst)
(sum '((A) (cos (*/ A pi 180.0))) Lst) )
180.0 pi ) )

(for L '((350.0 10.0) (90.0 180.0 270.0 360.0) (10.0 20.0 30.0))
(prinl
"The mean angle of ["
(glue ", " (mapcar round L '(0 .)))
"] is: " (round (meanAngle L))) )


{{out}}

The mean angle of [350, 10] is: 0.000
The mean angle of [90, 180, 270, 360] is: 90.000
The mean angle of [10, 20, 30] is: 20.000


## PL/I

averages: procedure options (main);             /* 31 August 2012 */
declare b1(2) fixed initial (350, 10);
declare b2(4) fixed initial (90, 180, 270, 360);
declare b3(3) fixed initial (10, 20, 30);

put edit ( b1) (f(7));
put edit ( ' mean=', mean(b1) )   (a, f(7) );
put skip edit ( b3) (f(7));
put edit ( ' mean=', mean(b3) )   (a, f(7) );
put skip edit ( b2) (f(7));
put edit ( ' mean=', mean(b2) )   (a, f(7) );

mean: procedure (a) returns (fixed);
declare a(*) float (18);
return ( atand(sum(sind(a))/hbound(a), sum(cosd(a))/hbound(a) ) );
end mean;

end averages;


Results (the final one brings up an error in inverse tangent):


350     10 mean=      0
10     20     30 mean=     20
90    180    270    360 mean=
IBM0683I  ONCODE=1521  X or Y in ATAN(X,Y) or ATAND(X,Y) was invalid.
At offset +000009CC in procedure with entry AVERAGES



## PowerShell


function Get-MeanAngle ([double[]]$Angles) {$x = ($Angles | ForEach-Object {[Math]::Cos($_ * [Math]::PI / 180)} | Measure-Object -Average).Average
$y = ($Angles | ForEach-Object {[Math]::Sin($_ * [Math]::PI / 180)} | Measure-Object -Average).Average [Math]::Atan2($y, $x) * 180 / [Math]::PI }   @(350, 10), @(90, 180, 270, 360), @(10, 20, 30) | ForEach-Object {Get-MeanAngle$_}



{{Out}}


-2.74517688449847E-14
-90
20



## Python

{{works with|Python|2.6+}}

 from cmath import rect, phase
>>> from math import radians, degrees
>>> def mean_angle(deg):
...     return degrees(phase(sum(rect(1, radians(d)) for d in deg)/len(deg)))
...
>>> for angles in [[350, 10], [90, 180, 270, 360], [10, 20, 30]]:
...     print('The mean angle of', angles, 'is:', round(mean_angle(angles), 12), 'degrees')
...
The mean angle of [350, 10] is: -0.0 degrees
The mean angle of [90, 180, 270, 360] is: -90.0 degrees
The mean angle of [10, 20, 30] is: 20.0 degrees
>>>


## Racket

The formula given above can be straightforwardly transcribed into a program:


#lang racket

(define (mean-angle αs)

(define n (length αs))
(atan (* (/ 1 n) (for/sum ([α_j αs]) (sin α_j)))
(* (/ 1 n) (for/sum ([α_j αs]) (cos α_j)))))

(mean-angle '(350 0 10))
(mean-angle '(90 180 270 360))
(mean-angle '(10 20 30))



{{out}}


-1.0710324872062297e-15
-90.0
19.999999999999996



## REXX

This REXX version uses an '''ATAN2''' solution.

The REXX language doesn't have most of the higher mathematical functions (like '''sqrt'''), and none of the trigonometric

functions, so all of them have to be included as RYO ('''R'''oll-'''Y'''our-'''O'''wn).


Note that the second set of angles:    90    180   270   360

is the same as:                        90    180   -90     0
and:                      -270   -180   -90  -360

and other combinations.



All the trigonometric functions use normalization (converting the angle to a unit circle) before computation, and most

of them use shortcuts for some exact values, so there is a minimum of errors due to rounding for ''near values'' for some

common values.

The consequence is the trig functions may return exact values such as '''0''' (zero) for '''sin(-2$\pi$)''' instead of '''-8.154E-61'''.

This very small difference (almost inconsequential) makes a significant difference when that value is used for a parameter

for the '''ATAN2''' function; in particular, the ''sign'' of the value.

There isn't much difference between: -8.154e-61 and +8.154e-61 in magnitude, but the '''ATAN2''' function treats those two numbers very differently as the angle will be in different quadrants,

thereby yielding a different value.

Usually this just results in an angle of '''-90º''' instead of '''+270º''' (both angles are equivalent).

Also note that the REXX subroutines are largely not commented as they provide a support structure that's normally present

into single lines would increase the program's bulk and detract from the main program.

/*REXX program  computes  the   mean angle   for a  group of angles  (expressed in degrees). */
call pi                                          /*define the value of  pi  to some accuracy.*/
numeric digits length(pi) - 1;                   /*use PI width  decimal digits of precision,*/
showDig= 10                              /*only display  ten  decimal digits.        */
#= 350 10         ;   say show(#, meanAngleD(#)) /*display mean angle (in degrees), 1st case.*/
#= 90 180 270 360 ;   say show(#, meanAngleD(#)) /*   "      "    "     "    "      2nd   "  */
#= 10 20 30       ;   say show(#, meanAngleD(#)) /*   "      "    "     "    "      3rd   "  */
exit                                             /*stick a fork in it, we're all done with it*/
/*───────────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: arg z,_,i; x=x*x;  do k=2 by 2 until p=z; p=z; _=-_*x/(k*(k+i)); z=z+_; end;  return z
$fuzz: return min(arg(1), max(1, digits() - arg(2) ) ) Acos: procedure; parse arg x; return pi() * .5 - Asin(x) Atan: parse arg x; if abs(x)=1 then return pi()*.25 * sign(x); return Asin(x/sqrt(1 + x*x)) d2d: return arg(1) // 360 d2r: return r2r(d2d(arg(1)) / 180 * pi() ) r2d: return d2d((r2r(arg(1)) / pi()) * 180) r2r: return arg(1) // (pi() * 2) pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862;return pi /*───────────────────────────────────────────────────────────────────────────────────────────*/ Asin: procedure; parse arg x 1 z 1 o 1 p; a= abs(x); aa= a * a if a>1 then call AsinErr x /*argument X is out of range.*/ if a >= sqrt(2) * .5 then return sign(x) * acos( sqrt(1 - aa), '-ASIN') do j=2 by 2 until p=z; p= z; o= o * aa * (j-1) / j; z= z +o / (j+1); end return z /* [↑] compute until no noise*/ /*───────────────────────────────────────────────────────────────────────────────────────────*/ Atan2: procedure; parse arg y,x; call pi; s= sign(y) select when x=0 then z= s * pi * .5 when x<0 then if y=0 then z= pi; else z= s * (pi - abs( Atan(y/x) ) ) otherwise z= s * Atan(y / x) end /*select*/; return z /*───────────────────────────────────────────────────────────────────────────────────────────*/ cos: procedure; parse arg x; x= r2r(x); numeric fuzz$fuzz(6, 3)
a= abs(x);      if a=0  then return   1;      if a=pi    then return -1
if a=pi*.5 | a= pi*1.5  then return   0;      if a=pi/3  then return .5
if a= pi*2/3  then return -.5;                      return .sinCos(1, 1, -1)
/*───────────────────────────────────────────────────────────────────────────────────────────*/
meanAngleD: procedure;  parse arg x;                  numeric digits digits() + digits() % 4
n= words(x);                              _sin= 0;              _cos= 0
do j=1  for n;  != d2r( word(x, j));   _sin= _sin + sin(!);  _cos= _cos + cos(!)
end   /*j*/
return  r2d( Atan2( _sin/n, _cos/n) )
/*───────────────────────────────────────────────────────────────────────────────────────────*/
show:   parse arg a,mA;                               _= format(ma, , showDig, 0) / 1
return left('angles='a, 30)   "mean angle="   right(_, max(4, length(_) ) )
/*───────────────────────────────────────────────────────────────────────────────────────────*/
if ( $x -$y ).abs() > $diff { panic!("floating point difference is to big {}",$x - $y ); } } } #[test] fn calculate() { let angles1 = [350.0_f64, 10.0]; let angles2 = [90.0_f64, 180.0, 270.0, 360.0]; let angles3 = [10.0_f64, 20.0, 30.0]; assert_diff!(0.0, mean_angle(&angles1), 0.001); assert_diff!(-90.0, mean_angle(&angles2), 0.001); assert_diff!(20.0, mean_angle(&angles3), 0.001); }  ## Scala {{libheader|Scala}} trait MeanAnglesComputation { import scala.math.{Pi, atan2, cos, sin} def meanAngle(angles: List[Double], convFactor: Double = 180.0 / Pi) = { val sums = angles.foldLeft((.0, .0))((r, c) => { val rads = c / convFactor (r._1 + sin(rads), r._2 + cos(rads)) }) val result = atan2(sums._1, sums._2) (result + (if (result.signum == -1) 2 * Pi else 0.0)) * convFactor } } object MeanAngles extends App with MeanAnglesComputation { assert(meanAngle(List(350, 10), 180.0 / math.Pi).round == 360, "Unexpected result with 350, 10") assert(meanAngle(List(90, 180, 270, 360)).round == 270, "Unexpected result with 90, 180, 270, 360") assert(meanAngle(List(10, 20, 30)).round == 20, "Unexpected result with 10, 20, 30") println("Successfully completed without errors.") }  ## Scheme {{trans|Common Lisp}}  (import (srfi 1 lists)) ;; use 'fold' from library (define (average l) (/ (fold + 0 l) (length l))) (define pi 3.14159265358979323846264338327950288419716939937510582097) (define (radians a) (* pi 1/180 a)) (define (degrees a) (* 180 (/ 1 pi) a)) (define (mean-angle angles) (let* ((angles (map radians angles)) (cosines (map cos angles)) (sines (map sin angles))) (degrees (atan (average sines) (average cosines))))) (for-each (lambda (angles) (display "The mean angle of ") (display angles) (display " is ") (display (mean-angle angles)) (newline)) '((350 10) (90 180 270 360) (10 20 30)))   The mean angle of (350 10) is -1.614809932057922E-15 The mean angle of (90 180 270 360) is -90.0 The mean angle of (10 20 30) is 19.999999999999996  ## Seed7 $ include "seed7_05.s7i";
include "float.s7i";
include "math.s7i";
include "complex.s7i";

const func float: deg2rad (in float: degree) is
return degree * PI / 180.0;

return rad * 180.0 / PI;

const func float: meanAngle (in array float: degrees) is func
result
var float: mean is 0.0;
local
var float: degree is 0.0;
var complex: sum is complex.value;
begin
for degree range degrees do
end for;
mean := rad2deg(arg(sum / complex conv length(degrees)));
end func;

const proc: main is func
begin
writeln(meanAngle([] (350.0, 10.0)) digits 4);
writeln(meanAngle([] (90.0, 180.0, 270.0, 360.0)) digits 4);
writeln(meanAngle([] (10.0, 20.0, 30.0)) digits 4);
end func;


{{out}} 0.0000 90.0000 20.0000

## Sidef

func mean_angle(angles) {
atan2(
}

[[350,10], [90,180,270,360], [10,20,30]].each { |angles|
say "The mean angle of #{angles.dump} is: #{ '%.2f' % mean_angle(angles)} degrees"
}


{{out}}


The mean angle of [350, 10] is: 0.00 degrees
The mean angle of [90, 180, 270, 360] is: -90.00 degrees
The mean angle of [10, 20, 30] is: 20.00 degrees



## Stata

mata
function meanangle(a) {
return(arg(sum(exp(C(0,a)))))
}

deg=pi()/180

meanangle((350,10)*deg)/deg
-1.61481e-15
meanangle((90,180,270,360)*deg)/deg
0
meanangle((10,20,30)*deg)/deg
20
end


## Tcl

proc meanAngle {angles} {
set toRadians [expr {atan2(0,-1) / 180}]
set sumSin [set sumCos 0.0]
foreach a $angles { set sumSin [expr {$sumSin + sin($a *$toRadians)}]
set sumCos [expr {$sumCos + cos($a * $toRadians)}] } # Don't need to divide by counts; atan2() cancels that out return [expr {atan2($sumSin, $sumCos) /$toRadians}]
}


Demonstration code:

# A little pretty-printer
proc printMeanAngle {angles} {
puts [format "mean angle of $%s$ = %.2f" \
[join $angles ", "] [meanAngle$angles]]
}

printMeanAngle {350 10}
printMeanAngle {90 180 270 360}
printMeanAngle {10 20 30}


{{out}}


mean angle of [350, 10] = -0.00
mean angle of [90, 180, 270, 360] = -90.00
mean angle of [10, 20, 30] = 20.00



## XPL0

include c:\cxpl\codes;

def Pi  = 3.14159265358979323846;
def D2R = Pi/180.0;             \coefficient to convert degrees to radians

func real MeanAng(A);           \Return the mean of the given list of angles
int  A;
real X, Y;
int  I;
[X:= 0.0;  Y:= 0.0;
for I:= 1 to A(0) do
[X:= X + Cos(D2R*float(A(I)));
Y:= Y + Sin(D2R*float(A(I)));
];
return ATan2(Y,X)/D2R;
];

[Format(5, 15);
RlOut(0, MeanAng([2, 350, 10]));  CrLf(0);
RlOut(0, MeanAng([4, 90, 180, 270, 360]));  CrLf(0);
RlOut(0, MeanAng([3, 10, 20, 30]));  CrLf(0);
]


{{out}}


-0.000000000000003
-90.000000000000000
20.000000000000000



The second example is interesting because it computes ATan2(0.,0.), which is undefined in mathematics (like division by zero), but the floating point processor in IBM-PC-type computers defines it as zero. The reason -90 gets displayed instead is due to small rounding errors (and another extra-mathematical concept, -0). In fact almost any angle can result because of slight rounding errors as Y and X both approach zero.

## VBA

Option Base 1
Private Function mean_angle(angles As Variant) As Double
Dim sins() As Double, coss() As Double
ReDim sins(UBound(angles))
ReDim coss(UBound(angles))
For i = LBound(angles) To UBound(angles)
Next i
mean_angle = WorksheetFunction.Degrees( _
WorksheetFunction.Atan2( _
WorksheetFunction.sum(coss), _
WorksheetFunction.sum(sins)))
End Function
Public Sub main()
Debug.Print Format(mean_angle([{350,10}]), "##0")
Debug.Print Format(mean_angle([{90, 180, 270, 360}]), "##0")
Debug.Print Format(mean_angle([{10, 20, 30}]), "##0")
End Sub


{{out}}

0
-90
20


## Visual Basic .NET

{{trans|C#}}

Imports System.Math

Module Module1

Function MeanAngle(angles As Double()) As Double
Dim x = angles.Sum(Function(a) Cos(a * PI / 180)) / angles.Length
Dim y = angles.Sum(Function(a) Sin(a * PI / 180)) / angles.Length
Return Atan2(y, x) * 180 / PI
End Function

Sub Main()
Dim printMean = Sub(x As Double()) Console.WriteLine("{0:0.###}", MeanAngle(x))
printMean({350, 10})
printMean({90, 180, 270, 360})
printMean({10, 20, 30})
End Sub

End Module


{{out}}

0
-90
20


## zkl

fcn meanA(a1,a2,etc){
n:=as.len();
(as.apply("sin").sum(0.0)/n)
.atan2(as.apply("cos").sum(0.0)/n)
.toDeg()
}


{{out}}


zkl: meanA(350,10)
-1.61481e-15
zkl: meanA(90,180,270,360)
-90
meanA(10,20,30)
20



[[Category:Geometry]]