Another update from ingydotnet^djgoku
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Ingy döt Net
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7604 changed files with 108452 additions and 22726 deletions
12
Task/Averages-Mean-angle/Clojure/averages-mean-angle-1.clj
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12
Task/Averages-Mean-angle/Clojure/averages-mean-angle-1.clj
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@ -0,0 +1,12 @@
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(defn mean-fn
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[k coll]
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(let [n (count coll)
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trig (get {:sin #(Math/sin %) :cos #(Math/cos %)} k)]
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(* (/ 1 n) (reduce + (map trig coll)))))
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(defn mean-angle
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[degrees]
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(let [radians (map #(Math/toRadians %) degrees)
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a (mean-fn :sin radians)
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b (mean-fn :cos radians)]
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(Math/toDegrees (Math/atan2 a b))))
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@ -0,0 +1,8 @@
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(mean-angle [350 10])
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;=> -1.614809932057922E-15
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(mean-angle [90 180 270 360])
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;=> -90.0
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(mean-angle [10 20 30])
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;=> 19.999999999999996
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@ -1 +1 @@
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avgAngleD=: (_1 { [: (**|)&.+.@(+/ % #)&.(*.inv) 1,.])&.(1r180p1&*)
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avgAngleD=: 360|(_1 { [: (**|)&.+.@(+/ % #)&.(*.inv) 1,.])&.(1r180p1&*)
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@ -3,4 +3,4 @@ toComplex=: *.inv NB. maps integer pairs
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mean=: +/ % # NB. calculate arithmetic mean
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roundComplex=: (* * |)&.+. NB. discard an extraneous least significant bit of precision from a complex value whose magnitude is in the vicinity of 1
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avgAngleR=: _1 { [: roundComplex@mean&.toComplex 1 ,. ] NB. calculate average angle in radians
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avgAngleD=: avgAngleR&.rfd
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avgAngleD=: 360|avgAngleR&.rfd NB. calculate average angle in degrees
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@ -4,3 +4,7 @@
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0
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avgAngleD 10 20 30
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20
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avgAngleD 20 350
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5
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avgAngleD 10 340
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355
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18
Task/Averages-Mean-angle/JavaScript/averages-mean-angle.js
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Task/Averages-Mean-angle/JavaScript/averages-mean-angle.js
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function sum(a) {
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s = 0;
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for (var i in a) s += a[i];
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return s;
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}
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function degToRad(a) {
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return Math.PI/180*a;
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}
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function meanAngleDeg(a) {
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return 180/Math.PI*Math.atan2(sum(a.map(degToRad).map(Math.sin))/a.length,sum(a.map(degToRad).map(Math.cos))/a.length);
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}
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var a = [350, 10], b = [90, 180, 270, 360], c =[10, 20, 30];
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console.log(meanAngleDeg(a));
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console.log(meanAngleDeg(b));
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console.log(meanAngleDeg(c));
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13
Task/Averages-Mean-angle/Lua/averages-mean-angle.lua
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Task/Averages-Mean-angle/Lua/averages-mean-angle.lua
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@ -0,0 +1,13 @@
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function meanAngle (angleList)
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local sumSin, sumCos = 0, 0
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for i, angle in pairs(angleList) do
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sumSin = sumSin + math.sin(math.rad(angle))
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sumCos = sumCos + math.cos(math.rad(angle))
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end
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local result = math.deg(math.atan2(sumSin, sumCos))
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return string.format("%.2f", result)
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end
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print(meanAngle({350, 10}))
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print(meanAngle({90, 180, 270, 360}))
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print(meanAngle({10, 20, 30}))
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@ -0,0 +1,32 @@
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MODULE MeanAngle;
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IMPORT
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M := LRealMath,
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Out;
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CONST
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toRads = M.pi / 180;
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toDegs = 180 / M.pi;
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VAR
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grades: ARRAY 64 OF LONGREAL;
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PROCEDURE Mean(g: ARRAY OF LONGREAL): LONGREAL;
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VAR
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i: INTEGER;
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sumSin, sumCos: LONGREAL;
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BEGIN
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i := 0;sumSin := 0.0;sumCos := 0.0;
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WHILE g[i] # 0.0 DO
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sumSin := sumSin + M.sin(g[i] * toRads);
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sumCos := sumCos + M.cos(g[i] * toRads);
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INC(i)
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END;
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RETURN M.arctan2(sumSin / i,sumCos / i);
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END Mean;
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BEGIN
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grades[0] := 350.0;grades[1] := 10.0;
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Out.LongRealFix(Mean(grades) * toDegs,15,9);Out.Ln;
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grades[0] := 90.0;grades[1] := 180.0;grades[2] := 270.0;grades[3] := 360.0;
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Out.LongRealFix(Mean(grades) * toDegs,15,9);Out.Ln;
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grades[0] := 10.0;grades[1] := 20.0;grades[2] := 30.0;grades[3] := 0.0;
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Out.LongRealFix(Mean(grades) * toDegs,15,9);Out.Ln;
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END MeanAngle.
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@ -1,56 +1,57 @@
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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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/*REXX program computes the mean angle (the angles expressed in degrees). */
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numeric digits 50 /*use 50 decimal digits of precision,*/
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showDig=10 /* but only display ten decimal 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; 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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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────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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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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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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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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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 more noise. */
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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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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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cos: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(6, 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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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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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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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
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numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
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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 h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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numeric digits d; return (g/1)i /*make complex if X < 0.*/
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