Just another update
This commit is contained in:
Ingy döt Net
parent
a25938f123
commit
00a190b0a6
6591 changed files with 94363 additions and 23227 deletions
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@ -4,10 +4,11 @@ MsgBox, % MeanAngle(Angles[1]) "`n"
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. MeanAngle(Angles[3])
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MeanAngle(a, x=0, y=0) {
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c := ATan(1) / 45
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for k, v in a
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static c := ATan(1) / 45
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for k, v in a {
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x += Cos(v * c) / a.MaxIndex()
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, y += Sin(v * c) / a.MaxIndex()
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y += Sin(v * c) / a.MaxIndex()
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}
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return atan2(x, y) / c
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}
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@ -1,10 +1,10 @@
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import std.stdio, std.algorithm, std.complex;
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import std.math: PI;
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auto radians(T)(in T d) pure nothrow { return d * PI / 180; }
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auto degrees(T)(in T r) pure nothrow { return r * 180 / PI; }
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auto radians(T)(in T d) pure nothrow @nogc { return d * PI / 180; }
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auto degrees(T)(in T r) pure nothrow @nogc { return r * 180 / PI; }
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real meanAngle(T)(in T[] D) pure nothrow {
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real meanAngle(T)(in T[] D) pure nothrow @nogc {
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immutable t = reduce!((a, d) => a + d.radians.expi)(0.complex, D);
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return (t / D.length).arg.degrees;
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}
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@ -0,0 +1,26 @@
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include std/console.e
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include std/mathcons.e
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sequence AngleList = {{350,10},{90,180,270,360},{10,20,30}}
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function atan2(atom y, atom x)
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return 2*arctan((sqrt(power(x,2)+power(y,2)) - x)/y)
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end function
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function MeanAngle(sequence angles)
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atom x = 0, y = 0
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integer l = length(angles)
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for i = 1 to length(angles) do
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x += cos(angles[i] * PI / 180)
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y += sin(angles[i] * PI / 180)
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end for
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return atan2(y / l, x / l) * 180 / PI
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end function
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for i = 1 to length(AngleList) do
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printf(1,"Mean Angle for set %d: %3.5f\n",{i,MeanAngle(AngleList[i])})
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end for
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if getc(0) then end if
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@ -1,22 +1,28 @@
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package main
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import (
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"fmt"
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"math"
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"math/cmplx"
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"fmt"
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"math"
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"math/cmplx"
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)
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func deg2rad(d float64) float64 { return d * math.Pi / 180 }
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func rad2deg(r float64) float64 { return r * 180 / math.Pi }
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func mean_angle(deg []float64) float64 {
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sum := 0i
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for _, x := range deg { sum += cmplx.Rect(1, deg2rad(x)) }
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return rad2deg(cmplx.Phase(sum))
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sum := 0i
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for _, x := range deg {
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sum += cmplx.Rect(1, deg2rad(x))
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}
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return rad2deg(cmplx.Phase(sum))
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}
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func main() {
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for _, angles := range [][]float64 {{350, 10}, {90, 180, 270, 360}, {10, 20, 30}} {
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fmt.Printf("The mean angle of %v is: %f degrees\n", angles, mean_angle(angles))
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}
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for _, angles := range [][]float64{
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{350, 10},
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{90, 180, 270, 360},
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{10, 20, 30},
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} {
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fmt.Printf("The mean angle of %v is: %f degrees\n", angles, mean_angle(angles))
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}
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}
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@ -1,9 +1,9 @@
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func mean_angle(deg []float64) float64 {
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var ss, sc float64
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for _, x := range deg {
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s, c := math.Sincos(x * math.Pi / 180)
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ss += s
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sc += c
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}
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return math.Atan2(ss, sc) * 180 / math.Pi
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var ss, sc float64
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for _, x := range deg {
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s, c := math.Sincos(x * math.Pi / 180)
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ss += s
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sc += c
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}
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return math.Atan2(ss, sc) * 180 / math.Pi
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}
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17
Task/Averages-Mean-angle/Haskell/averages-mean-angle-2.hs
Normal file
17
Task/Averages-Mean-angle/Haskell/averages-mean-angle-2.hs
Normal file
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@ -0,0 +1,17 @@
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-- file: trigdeg.fs
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deg2rad deg = deg*pi/180.0
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rad2deg rad = rad*180.0/pi
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sind = sin . deg2rad
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cosd = cos . deg2rad
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tand = tan . deg2rad
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atand = rad2deg . atan
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atan2d y x = rad2deg (atan2 y x )
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avg_angle angles = atan2d y x
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where
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y = mean (map sind angles)
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x = mean (map cosd angles)
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-- End of trigdeg.fs --------
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13
Task/Averages-Mean-angle/Logo/averages-mean-angle.logo
Normal file
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Task/Averages-Mean-angle/Logo/averages-mean-angle.logo
Normal file
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@ -0,0 +1,13 @@
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to mean_angle :angles
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local "avgsin
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make "avgsin quotient apply "sum map "sin :angles count :angles
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local "avgcos
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make "avgcos quotient apply "sum map "cos :angles count :angles
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output (arctan :avgcos :avgsin)
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end
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foreach [[350 10] [90 180 270 360] [10 20 30]] [
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print (sentence [The average of \(] ? [\) is] (mean_angle ?))
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]
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bye
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71
Task/Averages-Mean-angle/Pascal/averages-mean-angle.pascal
Normal file
71
Task/Averages-Mean-angle/Pascal/averages-mean-angle.pascal
Normal file
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@ -0,0 +1,71 @@
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program MeanAngle;
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{$IFDEF DELPHI}
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{$APPTYPE CONSOLE}
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{$ENDIF}
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uses
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math;// sincos and atan2
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type
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tAngles = array of double;
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function MeanAngle(const a:tAngles;cnt:longInt):double;
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// calculates mean angle.
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// returns 0.0 if direction is not sure.
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const
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eps = 1e-10;
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var
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i : LongInt;
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s,c,
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Sumsin,SumCos : extended;
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begin
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IF cnt = 0 then
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Begin
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MeanAngle := 0.0;
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EXIT;
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end;
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SumSin:= 0;
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SumCos:= 0;
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For i := Cnt-1 downto 0 do
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Begin
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sincos(DegToRad(a[i]),s,c);
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Sumsin := sumSin+s;
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SumCos := sumCos+c;
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end;
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s := SumSin/cnt;
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c := sumCos/cnt;
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IF c > eps then
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MeanAngle := RadToDeg(arctan2(s,c))
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else
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// Not meaningful
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MeanAngle := 0.0;
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end;
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Procedure OutMeanAngle(const a:tAngles;cnt:longInt);
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var
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i : longInt;
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Begin
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IF cnt > 0 then
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Begin
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write('The mean angle of [');
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For i := 0 to Cnt-2 do
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write(a[i]:0:2,',');
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write(a[Cnt-1]:0:2,'] => ');
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writeln(MeanAngle(a,cnt):0:16);
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end;
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end;
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var
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a:tAngles;
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Begin
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setlength(a,4);
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a[0] := 350;a[1] := 10;
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OutMeanAngle(a,2);
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a[0] := 90;a[1] := 180;a[2] := 270;a[3] := 360;
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OutMeanAngle(a,4);
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a[0] := 10;a[1] := 20;a[2] := 30;
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OutMeanAngle(a,3);
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setlength(a,0);
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end.
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17
Task/Averages-Mean-angle/Perl/averages-mean-angle.pl
Normal file
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Task/Averages-Mean-angle/Perl/averages-mean-angle.pl
Normal file
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@ -0,0 +1,17 @@
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sub Pi () { 3.1415926535897932384626433832795028842 }
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sub meanangle {
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my($x, $y) = (0,0);
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($x,$y) = ($x + sin($_), $y + cos($_)) for @_;
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my $atan = atan2($x,$y);
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$atan += 2*Pi while $atan < 0; # Ghetto fmod
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$atan -= 2*Pi while $atan > 2*Pi;
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$atan;
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}
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sub meandegrees {
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meanangle( map { $_ * Pi/180 } @_ ) * 180/Pi;
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}
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print "The mean angle of [@$_] is: ", meandegrees(@$_), " degrees\n"
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for ([350,10], [90,180,270,360], [10,20,30]);
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@ -1,57 +1,56 @@
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/*REXX program to compute the mean angle (angles expressed in degrees).*/
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numeric digits 50 /*use fifty digits of precision. */
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showDigs=10 /* ... but only show ten digits. */
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#=350 10 ; say showit(#, meanAngleD(#))
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#=90 180 270 360 ; say showit(#, meanAngleD(#))
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#=10 20 30 ; say showit(#, meanAngleD(#))
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/*REXX program computes the mean angle (angles expressed in degrees). */
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numeric digits 50 /*use fifty digits of precision, */
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showDig=10 /*··· but only display 10 digits.*/
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# = 350 10 ; say showit(#, meanAngleD(#) )
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# = 90 180 270 360 ; say showit(#, meanAngleD(#) )
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# = 10 20 30 ; say showit(#, meanAngleD(#) )
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────MEANANGD subroutine─────────────────*/
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meanAngleD: procedure; arg x; _sin=0; _cos=0
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numeric digits $d()+$d()%4
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n=words(x); do j=1 for n
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xr = d2r(d2d(word(x,j)))
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_sin = _sin + sin(xr)
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_cos = _cos + cos(xr)
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end /*j*/
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return r2d(atan2(_sin/n, _cos/n))
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/*═════════════════════════════general 1-line subs══════════════════════*/
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/*The 1-line subs were broken up into multiple lines for easier reading.*/
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d2d: return arg(1)//360
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d2r: return r2r(d2d(arg(1))/180*pi())
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r2d: return d2d((r2r(arg(1))/pi())*180)
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r2r: return arg(1)//(2*pi())
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p: return word(arg(1),1)
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$d: return p(arg(1) digits())
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$fuzz: return min(arg(1),max(1,$d()-arg(2)))
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showit: procedure expose showDigs; numeric digits showDigs; arg a,ma
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return left('angles='a,30) 'mean angle=' format(ma,,showDigs,0)/1
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acos: procedure; arg x; if x<-1 | x>1 then call $81r -1,1,x,"ACOS"
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return .5*pi() - asin(x) /* $81r subroutine not included here.*/
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atan: if abs(arg(1))=1 then return pi()*.25*sign(arg(1))
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return asin(arg(1) / sqrt(1+arg(1)**2))
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asin: procedure; arg x; if x<-1 | x>1 then call $81r -1,1,x,"ASIN"
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s=x*x; if abs(x)>=.7 then return sign(x)*acos(sqrt(1-s),'-ASIN')
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z=x; o=x; p=z; do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1)
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if z=p then leave; p=z; end; return z
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atan2: procedure; arg y,x; pi=pi(); s=sign(y)
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select; when x=0 then z=s*pi*.5; when x<0 then if y=0 then z=pi
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else z=s*(pi-abs(atan(y/x)));otherwise z=s*atan(y/x);end; return z
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cos: procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz $fuzz(5,3)
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if a=0 then return 1; if a=pi() then return -1
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if a=pi()*.5 | a=pi()*1.5 then return 0;if a=pi()/3 then return .5
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if a=2*pi()/3 then return -.5; return .sincos(1,1,-1)
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sin: procedure; arg x; x=r2r(x); numeric fuzz $fuzz(5,3)
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if x=pi()*.5 then return 1; if x==pi()*1.5 then return -1
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if abs(x)=pi() | x=0 then return 0; return .sincos(x,x,1)
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.sincos: parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_
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if z=p then leave; p=z; end; return z
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits()
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numeric digits 11; g=.sqrtGuess(); do j=0 while p>9;m.j=p; p=p%2+1
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end; do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
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g=.5*(g+x/g); end; numeric digits d; return g/1
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.sqrtGuess: if x<0 then call er 02,x p($.ff 'SQRT') "negative"
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/*The above IF statement was left here to show checking for x<0.*/
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numeric form; m.=11; p=d+d%4+2
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .;return g*.5'E'_%2
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pi: return ,
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3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148
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meanAngleD: procedure; parse arg x; numeric digits digits()+digits()%4
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_sin=0; _cos=0; n=words(x); do j=1 for n; !=d2r(word(x,j))
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_sin = _sin + sin(!)
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_cos = _cos + cos(!)
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end /*j*/
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return r2d(atan2(_sin/n, _cos/n))
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/*─────────────────────────────one─line subroutines──────────────────────────────────────────*/
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.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
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$fuzz: return min(arg(1), max(1, digits() - arg(2) ) )
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acos: procedure; parse arg x; return pi() * .5 - asin(x)
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atan: parse arg x; if abs(x)=1 then return pi()*.25 * sign(x); return asin(x/sqrt(1 + x*x))
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d2d: return arg(1) // 360
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d2r: return r2r(d2d(arg(1)) / 180 * pi() )
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r2d: return d2d((r2r(arg(1)) / pi()) * 180)
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r2r: return arg(1) // (pi() * 2)
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p: return word(arg(1), 1)
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pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862;return pi
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/*───────────────────────────────────ASIN subroutine────────────────────*/
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asin: procedure; parse arg x 1 z 1 o 1 p; xx=x*x
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if xx>=.5 then return sign(x) * acos(sqrt(1-xx))
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do j=2 by 2 until p=z; p=z; o=o*xx*(j-1)/j; z=z+o/(j+1); end
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return z /* [↑] compute until no noise.*/
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/*───────────────────────────────────ATAN2 subroutine───────────────────*/
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atan2: procedure; parse arg y,x; call pi; s=sign(y)
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select
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when x=0 then z=s * pi * .5
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when x<0 then if y=0 then z=pi; else z=s*(pi-abs(atan(y/x)))
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otherwise z=s * atan(y/x)
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end /*select*/; return z
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/*───────────────────────────────────COS subroutine─────────────────────*/
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cos: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
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a=abs(x); if a=0 then return 1; if a=pi then return -1
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if a=pi*.5 | a=pi*1.5 then return 0; if a=pi/3 then return .5
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if a=pi*2/3 then return -.5; return .sinCos(1, 1, -1)
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/*───────────────────────────────────SHOWIT subroutine──────────────────*/
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showit: procedure expose showDig; numeric digits showDig; parse arg a,mA
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return left('angles='a,30) 'mean angle=' format(mA,,showDig,0)/1
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/*───────────────────────────────────COS subroutine─────────────────────*/
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
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if x=pi*.5 then return 1; if x==pi*1.5 then return -1
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if abs(x)=pi | x=0 then return 0; return .sinCos(x, x, +1)
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/*───────────────────────────────────SQRT subroutine────────────────────*/
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sqrt: procedure; parse arg x,i; if x=0 then return 0; d=digits(); m.=11
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if x<0 then i='i'; numeric digits 11; numeric form; p=d+d%4+2
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'E'_%2
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do j=0 while p>9; m.j=p; p=p%2+1; end /*j*/
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do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
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g=.5*(g+x/g); end /*k*/; numeric digits d; return g/1
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19
Task/Averages-Mean-angle/Scala/averages-mean-angle.scala
Normal file
19
Task/Averages-Mean-angle/Scala/averages-mean-angle.scala
Normal file
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@ -0,0 +1,19 @@
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trait MeanAnglesComputation {
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import scala.math.{Pi, atan2, cos, sin}
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def meanAngle(angles: List[Double], convFactor: Double = 180.0 / Pi) = {
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val sums = angles.foldLeft((.0, .0))((r, c) => {
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val rads = c / convFactor
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(r._1 + sin(rads), r._2 + cos(rads))
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})
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val result = atan2(sums._1, sums._2)
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(result + (if (result.signum == -1) 2 * Pi else 0.0)) * convFactor
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}
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}
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object MeanAngles extends App with MeanAnglesComputation {
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assert(meanAngle(List(350, 10), 180.0 / math.Pi).round == 360, "Unexpected result with 350, 10")
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assert(meanAngle(List(90, 180, 270, 360)).round == 270, "Unexpected result with 90, 180, 270, 360")
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assert(meanAngle(List(10, 20, 30)).round == 20, "Unexpected result with 10, 20, 30")
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println("Successfully completed without errors.")
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}
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