Data update

Task/Averages-Mean-angle/Ada/averages-mean-angle.adb

@@ -0,0 +1,34 @@
+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
+      package IO is new Ada.Text_IO.Float_IO(Real);
+   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
+      package Math is new Ada.Numerics.Generic_Elementary_Functions(Real);
+      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((10.0, 350.0)));          Ada.Text_IO.New_Line;    --  0.00
+   Put(Mean_Angle((90.0, 180.0, 270.0, 360.0))); -- Ada.Numerics.Argument_Error!
+end Mean_Angles;

Task/Averages-Mean-angle/Crystal/averages-mean-angle.cr

@@ -0,0 +1,17 @@
+require "complex"
+
+def deg_to_rad (d)
+  d * Math::PI / 180
+end
+
+def rad_to_deg (r)
+  r * 180 / Math::PI
+end
+
+def mean_angle (angles)
+  rad_to_deg(angles.sum {|deg| deg_to_rad(deg).cis }.phase)
+end
+
+[[350, 10], [90, 180, 270, 360], [10, 20, 30]].each do |angles|
+  puts "The mean angle of %s is: %.2f°." % [angles, mean_angle(angles)]
+end

Task/Averages-Mean-angle/Euphoria/averages-mean-angle.eu

@@ -0,0 +1,26 @@
+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

Task/Averages-Mean-angle/Pluto/averages-mean-angle.pluto

@@ -0,0 +1,20 @@
+local fmt = require "fmt"
+
+local function mean_angle(angles)
+    local n = #angles
+    local sin_sum = 0
+    local cos_sum = 0
+    for angles as angle do
+        sin_sum += math.sin(angle * math.pi / 180.0)
+        cos_sum += math.cos(angle * math.pi / 180.0)
+    end
+    return math.atan(sin_sum / n, cos_sum / n) * 180.0 / math.pi
+end
+
+local angles1 = {350, 10}
+local angles2 = {90, 180, 270, 360}
+local angles3 = {10, 20, 30}
+
+for i, angles in {angles1, angles2, angles3} do
+    fmt.print("Mean for angles %d is : %6.2f", i, mean_angle(angles))
+end

Task/Averages-Mean-angle/PowerShell/averages-mean-angle-1.ps1

@@ -0,0 +1,7 @@
+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
+}

Task/Averages-Mean-angle/PowerShell/averages-mean-angle-2.ps1

@@ -0,0 +1 @@
+@(350, 10), @(90, 180, 270, 360), @(10, 20, 30) | ForEach-Object {Get-MeanAngle $_}

Task/Averages-Mean-angle/REXX/averages-mean-angle.rexx

@@ -1,55 +1,39 @@
-/*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(_) ) )
-/*───────────────────────────────────────────────────────────────────────────────────────────*/
-sin:    procedure; parse arg x;   x= r2r(x);          numeric fuzz  $fuzz(5, 3)
-        if x=pi * .5         then return 1;           if x==pi * 1.5  then return -1
-        if abs(x)=pi | x=0   then return 0;           return .sinCos(x, x, +1)
-/*───────────────────────────────────────────────────────────────────────────────────────────*/
-sqrt:   procedure; parse arg x; if x=0  then return 0;  d=digits();  m.=9; numeric form; h= d+6
-        numeric digits;  parse value format(x,2,1,,0) 'E0'  with  g "E" _ .;  g= g * .5'e'_ % 2
-                 do j=0  while h>9;       m.j= h;               h= h % 2  +  1;     end  /*j*/
-                 do k=j+5  to 0  by -1;   numeric digits m.k;   g= (g + x/g) * .5;  end  /*k*/
-        return g
+-- 21 Feb 2026
+include Setting
+
+say 'MEAN ANGLE'
+say version
+say
+numeric digits 11
+say 'Meaningful...'
+call Task '350;10'
+call Task '10;20;30'
+call Task '180'
+say
+say 'Mathematically undefined...'
+call Task '90;180;270;360'
+call Task '0;180'
+call Task '45;225'
+call Task '90;270'
+call Task '135;305'
+exit
+
+Task:
+procedure expose Memo.
+arg xx
+say 'Mean angle of list {'xx'} =' DegL(CmeanL(RadL(xx)))/1
+return
+
+CmeanL:
+-- Returns circular mean of a list
+procedure expose Memo.
+arg xx
+ss=0; sc=0
+do while xx<>''
+   parse var xx xw';'xx
+   ss+=Sin(xw); sc+=Cos(xw)
+end
+return Arctan2(sc,ss)
+
+-- CmeanL (full); DegL; RadL; Sin; Cos; Arctan2
+include Math

Task/Averages-Mean-angle/Scheme/averages-mean-angle-1.scm

@@ -0,0 +1,23 @@
+(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)))

Task/Averages-Mean-angle/Scheme/averages-mean-angle-2.scm

@@ -0,0 +1,24 @@
+(define pi (* 4 (atan 1)))
+
+(define (->radians d) (* d (/ pi 180)))
+(define (->degrees r) (* r (/ 180 pi)))
+
+(define (average-direction angles)
+  (->degrees
+   ;; find the angle of the sum in radians
+   (angle
+    (apply + (map (lambda (d)
+                    ;; a complex number on the unit circle
+                    (make-polar 1 (->radians d)))
+                  angles)))))
+
+(for-each (lambda (l)
+            (for-each display
+                      (list "The mean angle of "
+                        l
+                        " is "
+                        (average-direction l)
+                        #\newline)))
+          '((350 10)
+            (90 180 270 360)
+            (10 20 30)))