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---
from: http://rosettacode.org/wiki/Deming's_funnel

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[[wp:W. Edwards Deming|W Edwards Deming]] was an American statistician and management guru who used physical demonstrations to illuminate his teachings. In one demonstration Deming repeatedly dropped marbles through a funnel at a target, marking where they landed, and observing the resulting pattern. He applied a sequence of "rules" to try to improve performance. In each case the experiment begins with the funnel positioned directly over the target.
* '''Rule 1''': The funnel remains directly above the target.
* '''Rule 2''': Adjust the funnel position by shifting the target to compensate after each drop. E.g. If the last drop missed 1 cm east, move the funnel 1 cm to the west of its current position.
* '''Rule 3''': As rule 2, but first move the funnel back over the target, before making the adjustment. E.g. If the funnel is 2 cm north, and the marble lands 3 cm north, move the funnel 3 cm south of the target.
* '''Rule 4''': The funnel is moved directly over the last place a marble landed.
Apply the four rules to the set of 50 pseudorandom displacements provided (e.g in the Racket solution) for the dxs and dys. '''Output''': calculate the mean and standard-deviations of the resulting x and y values for each rule.
Note that rules 2, 3, and 4 give successively worse results. Trying to deterministically compensate for a random process is counter-productive, but -- according to Deming -- quite a popular pastime: see the Further Information, below for examples.
'''Stretch goal 1''': Generate fresh pseudorandom data. The radial displacement of the drop from the funnel position is given by a Gaussian distribution (standard deviation is 1.0) and the angle of displacement is uniformly distributed.
'''Stretch goal 2''': Show scatter plots of all four results.
;Further information:
* Further [http://blog.newsystemsthinking.com/w-edwards-deming-and-the-funnel-experiment/ explanation and interpretation]
* [https://www.youtube.com/watch?v=2VogtYRc9dA Video demonstration] of the funnel experiment at the Mayo Clinic.

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V dxs = [-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275, 1.251,
-0.231, -0.401, 0.269, 0.491, 0.951, 1.15, 0.001, -0.382, 0.161, 0.915,
2.08, -2.337, 0.034, -0.126, 0.014, 0.709, 0.129, -1.093, -0.483, -1.193,
0.02, -0.051, 0.047, -0.095, 0.695, 0.34, -0.182, 0.287, 0.213, -0.423,
-0.021, -0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315, 0.201,
0.034, 0.097, -0.17, 0.054, -0.553, -0.024, -0.181, -0.7, -0.361, -0.789,
0.279, -0.174, -0.009, -0.323, -0.658, 0.348, -0.528, 0.881, 0.021, -0.853,
0.157, 0.648, 1.774, -1.043, 0.051, 0.021, 0.247, -0.31, 0.171, 0.0, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017, 0.281, -0.749,
-0.149, -2.436, -0.909, 0.394, -0.113, -0.598, 0.443, -0.521, -0.799,
0.087]
V dys = [0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395, 0.49, -0.682,
-0.065, 0.242, -0.288, 0.658, 0.459, 0.0, 0.426, 0.205, -0.765, -2.188,
-0.742, -0.01, 0.089, 0.208, 0.585, 0.633, -0.444, -0.351, -1.087, 0.199,
0.701, 0.096, -0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.79, 0.723, 0.881, -0.508, 0.393, -0.226, 0.71, 0.038,
-0.217, 0.831, 0.48, 0.407, 0.447, -0.295, 1.126, 0.38, 0.549, -0.445,
-0.046, 0.428, -0.074, 0.217, -0.822, 0.491, 1.347, -0.141, 1.23, -0.044,
0.079, 0.219, 0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.65, -1.103, 0.154, -1.72, 0.051, -0.385, 0.477, 1.537, -0.901,
0.939, -0.411, 0.341, -0.411, 0.106, 0.224, -0.947, -1.424, -0.542, -1.032]
F funnel(dxs, rule)
V x = 0.0
[Float] rxs
L(dx) dxs
rxs.append(x + dx)
x = rule(x, dx)
R rxs
F mean(xs)
R sum(xs) / xs.len
F stddev(xs)
V m = mean(xs)
R sqrt(sum(xs.map(x -> (x - @m) ^ 2)) / xs.len)
F experiment(label, rule)
V (rxs, rys) = (funnel(:dxs, rule), funnel(:dys, rule))
print(label)
print(‘Mean x, y : #.4, #.4’.format(mean(rxs), mean(rys)))
print(‘Std dev x, y : #.4, #.4’.format(stddev(rxs), stddev(rys)))
print()
experiment(‘Rule 1:’, (z, dz) -> 0)
experiment(‘Rule 2:’, (z, dz) -> -dz)
experiment(‘Rule 3:’, (z, dz) -> -(z + dz))
experiment(‘Rule 4:’, (z, dz) -> z + dz)

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with Ada.Numerics.Elementary_Functions;
with Ada.Text_IO;
procedure Demings_Funnel is
type Float_List is array (Positive range <>) of Float;
Dxs : constant Float_List :=
(-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087);
Dys : constant Float_List :=
( 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032);
type Rule_Access is access function (Z, Dz : Float) return Float;
function Funnel (List : in Float_List;
Rule : in Rule_Access)
return Float_List
is
Correc : Float := 0.0;
Result : Float_List (List'Range);
begin
for I in List'Range loop
Result (I) := Correc + List (I);
Correc := Rule (Correc, List (I));
end loop;
return Result;
end Funnel;
function Mean (List : in Float_List)
return Float
is
Sum : Float := 0.0;
begin
for Value of List loop
Sum := Sum + Value;
end loop;
return Sum / Float (List'Length);
end Mean;
function Stddev (List : in Float_List)
return Float
is
use Ada.Numerics.Elementary_Functions;
M : constant Float := Mean (List);
Sum : Float := 0.0;
begin
for F of List loop
Sum := Sum + (F - M) * (F - M);
end loop;
return Sqrt (Sum / Float (List'Length));
end Stddev;
procedure Experiment (Label : in String;
Rule : in Rule_Access)
is
package Float_IO is new Ada.Text_IO.Float_IO (Float);
use Ada.Text_IO;
use Float_IO;
Rxs : constant Float_List := Funnel (Dxs, Rule);
Rys : constant Float_List := Funnel (Dys, Rule);
begin
Default_Exp := 0;
Default_Fore := 4;
Default_Aft := 4;
Put_Line (Label & " : x y");
Put ("Mean: "); Put (Mean (Rxs)); Put (Mean (Rys)); New_Line;
Put ("StdDev: "); Put (Stddev (Rxs)); Put (Stddev (Rys)); New_Line;
New_Line;
end Experiment;
function Rule_1 (Z, Dz : Float) return Float is (0.0);
function Rule_2 (Z, Dz : Float) return Float is (-Dz);
function Rule_3 (Z, Dz : Float) return Float is (-Z - Dz);
function Rule_4 (Z, Dz : Float) return Float is (Z + Dz);
begin
Experiment ("Rule 1", Rule_1'Access);
Experiment ("Rule 2", Rule_2'Access);
Experiment ("Rule 3", Rule_3'Access);
Experiment ("Rule 4", Rule_4'Access);
end Demings_Funnel;

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Dxs: @[
neg 0.533, 0.270, 0.859, neg 0.043, neg 0.205, neg 0.127, neg 0.071, 0.275,
1.251, neg 0.231, neg 0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
neg 0.382, 0.161, 0.915, 2.080, neg 2.337, 0.034, neg 0.126, 0.014,
0.709, 0.129, neg 1.093, neg 0.483, neg 1.193, 0.020, neg 0.051, 0.047,
neg 0.095, 0.695, 0.340, neg 0.182, 0.287, 0.213, neg 0.423, neg 0.021,
neg 0.134, 1.798, 0.021, neg 1.099, neg 0.361, 1.636, neg 1.134, 1.315,
0.201, 0.034, 0.097, neg 0.170, 0.054, neg 0.553, neg 0.024, neg 0.181,
neg 0.700, neg 0.361, neg 0.789, 0.279, neg 0.174, neg 0.009, neg 0.323, neg 0.658,
0.348, neg 0.528, 0.881, 0.021, neg 0.853, 0.157, 0.648, 1.774,
neg 1.043, 0.051, 0.021, 0.247, neg 0.310, 0.171, 0.000, 0.106,
0.024, neg 0.386, 0.962, 0.765, neg 0.125, neg 0.289, 0.521, 0.017,
0.281, neg 0.749, neg 0.149, neg 2.436, neg 0.909, 0.394, neg 0.113, neg 0.598,
0.443, neg 0.521, neg 0.799, 0.087
]
Dys: @[
0.136, 0.717, 0.459, neg 0.225, 1.392, 0.385, 0.121, neg 0.395,
0.490, neg 0.682, neg 0.065, 0.242, neg 0.288, 0.658, 0.459, 0.000,
0.426, 0.205, neg 0.765, neg 2.188, neg 0.742, neg 0.010, 0.089, 0.208,
0.585, 0.633, neg 0.444, neg 0.351, neg 1.087, 0.199, 0.701, 0.096,
neg 0.025, neg 0.868, 1.051, 0.157, 0.216, 0.162, 0.249, neg 0.007,
0.009, 0.508, neg 0.790, 0.723, 0.881, neg 0.508, 0.393, neg 0.226,
0.710, 0.038, neg 0.217, 0.831, 0.480, 0.407, 0.447, neg 0.295,
1.126, 0.380, 0.549, neg 0.445, neg 0.046, 0.428, neg 0.074, 0.217,
neg 0.822, 0.491, 1.347, neg 0.141, 1.230, neg 0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
neg 0.729, 0.650, neg 1.103, 0.154, neg 1.720, 0.051, neg 0.385, 0.477,
1.537, neg 0.901, 0.939, neg 0.411, 0.341, neg 0.411, 0.106, 0.224,
neg 0.947, neg 1.424, neg 0.542, neg 1.032
]
funnel: function [a, rule][
x: 0.0
result: []
loop a 'val [
'result ++ x + val
x: do rule
]
return result
]
formatFloat: function [f]->
to :string .format:"7.4f" f
experiment: function [label, rule][
rxs: funnel Dxs rule
rys: funnel Dys rule
print label
print repeat "=" 30
print ["Mean x,y :" formatFloat average rxs, formatFloat average rys]
print ["Std.dev x,y :" formatFloat deviation rxs, formatFloat deviation rys]
print ""
]
experiment "Rule 1" [0.0]
experiment "Rule 2" [neg val]
experiment "Rule 3" [neg x + val]
experiment "Rule 4" [x + val]

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import std.stdio, std.math, std.algorithm, std.range, std.typecons;
auto mean(T)(in T[] xs) pure nothrow @nogc {
return xs.sum / xs.length;
}
auto stdDev(T)(in T[] xs) pure nothrow {
immutable m = xs.mean;
return sqrt(xs.map!(x => (x - m) ^^ 2).sum / xs.length);
}
alias TF = double function(in double, in double) pure nothrow @nogc;
auto funnel(T)(in T[] dxs, in T[] dys, in TF rule) {
T x = 0, y = 0;
immutable(T)[] rxs, rys;
foreach (const dx, const dy; zip(dxs, dys)) {
immutable rx = x + dx;
immutable ry = y + dy;
x = rule(x, dx);
y = rule(y, dy);
rxs ~= rx;
rys ~= ry;
}
return tuple!("x", "y")(rxs, rys);
}
void experiment(T)(in string label,
in T[] dxs, in T[] dys, in TF rule) {
//immutable (rxs, rys) = funnel(dxs, dys, rule);
immutable rs = funnel(dxs, dys, rule);
label.writeln;
writefln("Mean x, y: %.4f, %.4f", rs.x.mean, rs.y.mean);
writefln("Std dev x, y: %.4f, %.4f", rs.x.stdDev, rs.y.stdDev);
writeln;
}
void main() {
immutable dxs = [
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087];
immutable dys = [
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032];
static assert(dxs.length == dys.length);
experiment("Rule 1:", dxs, dys, (z, dz) => 0.0);
experiment("Rule 2:", dxs, dys, (z, dz) => -dz);
experiment("Rule 3:", dxs, dys, (z, dz) => -(z + dz));
experiment("Rule 4:", dxs, dys, (z, dz) => z + dz);
}

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defmodule Deming do
def funnel(dxs, rule) do
{_, rxs} = Enum.reduce(dxs, {0, []}, fn dx,{x,rxs} ->
{rule.(x, dx), [x + dx | rxs]}
end)
rxs
end
def mean(xs), do: Enum.sum(xs) / length(xs)
def stddev(xs) do
m = mean(xs)
Enum.reduce(xs, 0.0, fn x,sum -> sum + (x-m)*(x-m) / length(xs) end)
|> :math.sqrt
end
def experiment(label, dxs, dys, rule) do
{rxs, rys} = {funnel(dxs, rule), funnel(dys, rule)}
IO.puts label
:io.format "Mean x, y : ~7.4f, ~7.4f~n", [mean(rxs), mean(rys)]
:io.format "Std dev x, y : ~7.4f, ~7.4f~n~n", [stddev(rxs), stddev(rys)]
end
end
dxs = [ -0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087]
dys = [ 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032]
Deming.experiment("Rule 1:", dxs, dys, fn _z, _dz -> 0 end)
Deming.experiment("Rule 2:", dxs, dys, fn _z, dz -> -dz end)
Deming.experiment("Rule 3:", dxs, dys, fn z, dz -> -(z+dz) end)
Deming.experiment("Rule 4:", dxs, dys, fn z, dz -> z+dz end)

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USING: combinators formatting generalizations grouping.extras io
kernel math math.statistics sequences ;
: show ( seq1 seq2 -- )
[ [ mean ] bi@ ] [ [ population-std ] bi@ ] 2bi
"Mean x, y : %.4f, %.4f\nStd dev x, y : %.4f, %.4f\n"
printf ;
{
-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275
1.251 -0.231 -0.401 0.269 0.491 0.951 1.150 0.001
-0.382 0.161 0.915 2.080 -2.337 0.034 -0.126 0.014
0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051 0.047
-0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021
-0.134 1.798 0.021 -1.099 -0.361 1.636 -1.134 1.315
0.201 0.034 0.097 -0.170 0.054 -0.553 -0.024 -0.181
-0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323 -0.658
0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774
-1.043 0.051 0.021 0.247 -0.310 0.171 0.000 0.106
0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521 0.017
0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
0.443 -0.521 -0.799 0.087
}
{
0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395
0.490 -0.682 -0.065 0.242 -0.288 0.658 0.459 0.000
0.426 0.205 -0.765 -2.188 -0.742 -0.010 0.089 0.208
0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096
-0.025 -0.868 1.051 0.157 0.216 0.162 0.249 -0.007
0.009 0.508 -0.790 0.723 0.881 -0.508 0.393 -0.226
0.710 0.038 -0.217 0.831 0.480 0.407 0.447 -0.295
1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217
-0.822 0.491 1.347 -0.141 1.230 -0.044 0.079 0.219
0.698 0.275 0.056 0.031 0.421 0.064 0.721 0.104
-0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477
1.537 -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224
-0.947 -1.424 -0.542 -1.032
}
{
[ "Rule 1:" print ]
[ "Rule 2:" print [ [ [ swap neg + ] 2clump-map ] [ first suffix ] bi ] bi@ ]
[ "Rule 3:" print [ 0 [ - neg ] accumulate* ] bi@ ]
[ "Rule 4:" print [ cum-sum ] bi@ ]
} [ show ] map-compose 2cleave

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Task/Demings-funnel/Go/demings-funnel.go Normal file
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package main
import (
"fmt"
"math"
)
type rule func(float64, float64) float64
var dxs = []float64{
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087,
}
var dys = []float64{
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032,
}
func funnel(fa []float64, r rule) []float64 {
x := 0.0
result := make([]float64, len(fa))
for i, f := range fa {
result[i] = x + f
x = r(x, f)
}
return result
}
func mean(fa []float64) float64 {
sum := 0.0
for _, f := range fa {
sum += f
}
return sum / float64(len(fa))
}
func stdDev(fa []float64) float64 {
m := mean(fa)
sum := 0.0
for _, f := range fa {
sum += (f - m) * (f - m)
}
return math.Sqrt(sum / float64(len(fa)))
}
func experiment(label string, r rule) {
rxs := funnel(dxs, r)
rys := funnel(dys, r)
fmt.Println(label, " : x y")
fmt.Printf("Mean : %7.4f, %7.4f\n", mean(rxs), mean(rys))
fmt.Printf("Std Dev : %7.4f, %7.4f\n", stdDev(rxs), stdDev(rys))
fmt.Println()
}
func main() {
experiment("Rule 1", func(_, _ float64) float64 {
return 0.0
})
experiment("Rule 2", func(_, dz float64) float64 {
return -dz
})
experiment("Rule 3", func(z, dz float64) float64 {
return -(z + dz)
})
experiment("Rule 4", func(z, dz float64) float64 {
return z + dz
})
}

57
Task/Demings-funnel/Haskell/demings-funnel.hs Normal file
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import Data.List (mapAccumL, genericLength)
import Text.Printf
funnel :: (Num a) => (a -> a -> a) -> [a] -> [a]
funnel rule = snd . mapAccumL (\x dx -> (rule x dx, x + dx)) 0
mean :: (Fractional a) => [a] -> a
mean xs = sum xs / genericLength xs
stddev :: (Floating a) => [a] -> a
stddev xs = sqrt $ sum [(x-m)**2 | x <- xs] / genericLength xs where
m = mean xs
experiment :: String -> [Double] -> [Double] -> (Double -> Double -> Double) -> IO ()
experiment label dxs dys rule = do
let rxs = funnel rule dxs
rys = funnel rule dys
putStrLn label
printf "Mean x, y : %7.4f, %7.4f\n" (mean rxs) (mean rys)
printf "Std dev x, y : %7.4f, %7.4f\n" (stddev rxs) (stddev rys)
putStrLn ""
dxs = [ -0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087]
dys = [ 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032]
main :: IO ()
main = do
experiment "Rule 1:" dxs dys (\_ _ -> 0)
experiment "Rule 2:" dxs dys (\_ dz -> -dz)
experiment "Rule 3:" dxs dys (\z dz -> -(z+dz))
experiment "Rule 4:" dxs dys (\z dz -> z+dz)

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Task/Demings-funnel/J/demings-funnel.j Normal file
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dx=:".0 :0-.LF
_0.533 0.270 0.859 _0.043 _0.205 _0.127 _0.071 0.275
1.251 _0.231 _0.401 0.269 0.491 0.951 1.150 0.001
_0.382 0.161 0.915 2.080 _2.337 0.034 _0.126 0.014
0.709 0.129 _1.093 _0.483 _1.193 0.020 _0.051 0.047
_0.095 0.695 0.340 _0.182 0.287 0.213 _0.423 _0.021
_0.134 1.798 0.021 _1.099 _0.361 1.636 _1.134 1.315
0.201 0.034 0.097 _0.170 0.054 _0.553 _0.024 _0.181
_0.700 _0.361 _0.789 0.279 _0.174 _0.009 _0.323 _0.658
0.348 _0.528 0.881 0.021 _0.853 0.157 0.648 1.774
_1.043 0.051 0.021 0.247 _0.310 0.171 0.000 0.106
0.024 _0.386 0.962 0.765 _0.125 _0.289 0.521 0.017
0.281 _0.749 _0.149 _2.436 _0.909 0.394 _0.113 _0.598
0.443 _0.521 _0.799 0.087
)
dy=:".0 :0-.LF
0.136 0.717 0.459 _0.225 1.392 0.385 0.121 _0.395
0.490 _0.682 _0.065 0.242 _0.288 0.658 0.459 0.000
0.426 0.205 _0.765 _2.188 _0.742 _0.010 0.089 0.208
0.585 0.633 _0.444 _0.351 _1.087 0.199 0.701 0.096
_0.025 _0.868 1.051 0.157 0.216 0.162 0.249 _0.007
0.009 0.508 _0.790 0.723 0.881 _0.508 0.393 _0.226
0.710 0.038 _0.217 0.831 0.480 0.407 0.447 _0.295
1.126 0.380 0.549 _0.445 _0.046 0.428 _0.074 0.217
_0.822 0.491 1.347 _0.141 1.230 _0.044 0.079 0.219
0.698 0.275 0.056 0.031 0.421 0.064 0.721 0.104
_0.729 0.650 _1.103 0.154 _1.720 0.051 _0.385 0.477
1.537 _0.901 0.939 _0.411 0.341 _0.411 0.106 0.224
_0.947 _1.424 _0.542 _1.032
)
Rule1=: ]
Rule2=: -/\.&.|.
Rule3=: ]-0,}:
Rule4=: ]+0,}:
smoutput ' Rule 1 (x,y):'
smoutput ' Mean: ',":dx ,&mean&Rule1 dy
smoutput ' Std dev: ',":dx ,&stddev&Rule1 dy
smoutput ' '
smoutput ' Rule 2 (x,y):'
smoutput ' Mean: ',":dx ,&mean&Rule2 dy
smoutput ' Std dev: ',":dx ,&stddev&Rule2 dy
smoutput ' '
smoutput ' Rule 3 (x,y):'
smoutput ' Mean: ',":dx ,&mean&Rule3 dy
smoutput ' Std dev: ',":dx ,&stddev&Rule3 dy
smoutput ' '
smoutput ' Rule 4 (x,y):'
smoutput ' Mean: ',":dx ,&mean&Rule4 dy
smoutput ' Std dev: ',":dx ,&stddev&Rule4 dy

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Task/Demings-funnel/Java/demings-funnel.java Normal file
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import static java.lang.Math.*;
import java.util.Arrays;
import java.util.function.BiFunction;
public class DemingsFunnel {
public static void main(String[] args) {
double[] dxs = {
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087};
double[] dys = {
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032};
experiment("Rule 1:", dxs, dys, (z, dz) -> 0.0);
experiment("Rule 2:", dxs, dys, (z, dz) -> -dz);
experiment("Rule 3:", dxs, dys, (z, dz) -> -(z + dz));
experiment("Rule 4:", dxs, dys, (z, dz) -> z + dz);
}
static void experiment(String label, double[] dxs, double[] dys,
BiFunction<Double, Double, Double> rule) {
double[] resx = funnel(dxs, rule);
double[] resy = funnel(dys, rule);
System.out.println(label);
System.out.printf("Mean x, y: %.4f, %.4f%n", mean(resx), mean(resy));
System.out.printf("Std dev x, y: %.4f, %.4f%n", stdDev(resx), stdDev(resy));
System.out.println();
}
static double[] funnel(double[] input, BiFunction<Double, Double, Double> rule) {
double x = 0;
double[] result = new double[input.length];
for (int i = 0; i < input.length; i++) {
double rx = x + input[i];
x = rule.apply(x, input[i]);
result[i] = rx;
}
return result;
}
static double mean(double[] xs) {
return Arrays.stream(xs).sum() / xs.length;
}
static double stdDev(double[] xs) {
double m = mean(xs);
return sqrt(Arrays.stream(xs).map(x -> pow((x - m), 2)).sum() / xs.length);
}
}

13
Task/Demings-funnel/Jq/demings-funnel-1.jq Normal file
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def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
# Simplistic approach:
def round($ndec): pow(10;$ndec) as $p | . * $p | round / $p;
# Emit {mean, ssdev, std} where std is (ssdev/length|sqrt)
def basic_statistics:
. as $in
| length as $length
| (add / $length) as $mean
| { $mean,
ssdev: (reduce $in[] as $x (0; . + (($x - $mean) | .*.))) }
| .std = ((.ssdev / $length ) | sqrt);

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Task/Demings-funnel/Jq/demings-funnel-2.jq Normal file
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def dxs: [
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087
];
def dys: [
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032
];
# fa is an array
# r is an expression that expects [x,f] as input
def funnel(fa; r):
{ x: 0, res: []}
| reduce range(0;fa|length) as $i (.;
fa[$i] as $f
| .res[$i] = .x + $f
| .x |= ([., $f] | r ) )
| .res;
# r is an expression as per `funnel`
def experiment(alabel; r):
def pp: round(4) | lpad(8);
(funnel(dxs; r) | basic_statistics) as $x
| (funnel(dys; r) | basic_statistics) as $y
| "\(alabel) : x y",
"Mean : \($x.mean|pp) \($y.mean|pp)",
"Std Dev : \($x.std|pp) \($y.std|pp)" ;
def task:
experiment("\nRule 1"; 0 ),
experiment("\nRule 2"; -.[1] ),
experiment("\nRule 3"; - add),
experiment("\nRule 4"; add ) ;
task

55
Task/Demings-funnel/Julia/demings-funnel.julia Normal file
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# Run from Julia REPL to see the plots.
using Statistics, Distributions, Plots
const racket_xdata = [-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275, 1.251, -0.231,
-0.401, 0.269, 0.491, 0.951, 1.150, 0.001, -0.382, 0.161, 0.915, 2.080, -2.337,
0.034, -0.126, 0.014, 0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051,
0.047, -0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021, -0.134, 1.798,
0.021, -1.099, -0.361, 1.636, -1.134, 1.315, 0.201, 0.034, 0.097, -0.170, 0.054,
-0.553, -0.024, -0.181, -0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323,
-0.658, 0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774, -1.043, 0.051,
0.021, 0.247, -0.310, 0.171, 0.000, 0.106, 0.024, -0.386, 0.962, 0.765, -0.125,
-0.289, 0.521, 0.017, 0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087]
const racket_ydata = [0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395, 0.490, -0.682, -0.065,
0.242, -0.288, 0.658, 0.459, 0.000, 0.426, 0.205, -0.765, -2.188, -0.742, -0.010,
0.089, 0.208, 0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096, -0.025,
-0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007, 0.009, 0.508, -0.790, 0.723,
0.881, -0.508, 0.393, -0.226, 0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447,
-0.295, 1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217, -0.822, 0.491,
1.347, -0.141, 1.230, -0.044, 0.079, 0.219, 0.698, 0.275, 0.056, 0.031, 0.421, 0.064,
0.721, 0.104, -0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477, 1.537,
-0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224, -0.947, -1.424, -0.542, -1.032]
const rules = [(x, y, dx, dy) -> [0, 0], (x, y, dx, dy) -> [-dx, -dy],
(x, y, dx, dy) -> [-x - dx, -y - dy], (x, y, dx, dy) -> [x + dx, y + dy]]
const plots, colors = plot(layout=(1,2)), [:red, :green, :blue, :yellow]
function makedata()
radius_angles = zip(rand(Normal(), 100), rand(Uniform(-π, π), 100))
zip([z[1] * cos(z[2]) for z in radius_angles], [z[1] * sin(z[2]) for z in radius_angles])
end
function testfunnel(useracket=true)
for (i, rule) in enumerate(rules)
origin = [0.0, 0.0]
xvec, yvec = Float64[], Float64[]
for point in (useracket ? zip(racket_xdata, racket_ydata) : makedata())
push!(xvec, origin[1] + point[1])
push!(yvec, origin[2] + point[2])
origin .= rule(origin[1], origin[2], point[1], point[2])
end
println("Rule $i results:")
println("mean x: ", round(mean(xvec), digits=4), " std x: ", round(std(xvec, corrected=false), digits=4),
" mean y: ", round(mean(yvec), digits=4), " std y: ", round(std(yvec, corrected=false), digits=4))
scatter!(xvec, yvec, color=colors[i], subplot=(useracket ? 1 : 2),
title= useracket ? "Racket Data" : "Random Data", label="Rule $i")
end
end
println("\nUsing Racket data.")
testfunnel()
println("\nUsing new data.")
testfunnel(false)
display(plots)

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Task/Demings-funnel/Kotlin/demings-funnel.kotlin Normal file
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// version 1.1.3
typealias Rule = (Double, Double) -> Double
val dxs = doubleArrayOf(
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087
)
val dys = doubleArrayOf(
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032
)
fun funnel(da: DoubleArray, rule: Rule): DoubleArray {
var x = 0.0
val result = DoubleArray(da.size)
for ((i, d) in da.withIndex()) {
result[i] = x + d
x = rule(x, d)
}
return result
}
fun mean(da: DoubleArray) = da.average()
fun stdDev(da: DoubleArray): Double {
val m = mean(da)
return Math.sqrt(da.map { (it - m) * (it - m) }.average())
}
fun experiment(label: String, rule: Rule) {
val rxs = funnel(dxs, rule)
val rys = funnel(dys, rule)
println("$label : x y")
println("Mean : ${"%7.4f, %7.4f".format(mean(rxs), mean(rys))}")
println("Std Dev : ${"%7.4f, %7.4f".format(stdDev(rxs), stdDev(rys))}")
println()
}
fun main(args: Array<String>) {
experiment("Rule 1") { _, _ -> 0.0 }
experiment("Rule 2") { _, dz -> -dz }
experiment("Rule 3") { z, dz -> -(z + dz) }
experiment("Rule 4") { z, dz -> z + dz }
}

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dxs = {-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.15, 0.001, -0.382,
0.161, 0.915, 2.08, -2.337, 0.034, -0.126, 0.014, 0.709,
0.129, -1.093, -0.483, -1.193, 0.02, -0.051, 0.047, -0.095, 0.695,
0.34, -0.182, 0.287, 0.213, -0.423, -0.021, -0.134, 1.798,
0.021, -1.099, -0.361, 1.636, -1.134, 1.315, 0.201, 0.034,
0.097, -0.17, 0.054, -0.553, -0.024, -0.181, -0.7, -0.361, -0.789,
0.279, -0.174, -0.009, -0.323, -0.658, 0.348, -0.528, 0.881,
0.021, -0.853, 0.157, 0.648, 1.774, -1.043, 0.051, 0.021,
0.247, -0.31, 0.171, 0., 0.106, 0.024, -0.386, 0.962,
0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087};
dys = {0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.49, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0., 0.426,
0.205, -0.765, -2.188, -0.742, -0.01, 0.089, 0.208, 0.585,
0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096, -0.025, -0.868,
1.051, 0.157, 0.216, 0.162, 0.249, -0.007, 0.009, 0.508, -0.79,
0.723, 0.881, -0.508, 0.393, -0.226, 0.71, 0.038, -0.217, 0.831,
0.48, 0.407, 0.447, -0.295, 1.126, 0.38, 0.549, -0.445, -0.046,
0.428, -0.074, 0.217, -0.822, 0.491, 1.347, -0.141, 1.23, -0.044,
0.079, 0.219, 0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721,
0.104, -0.729, 0.65, -1.103, 0.154, -1.72, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106,
0.224, -0.947, -1.424, -0.542, -1.032};
(*Mathematica's StandardDeviation function computes the unbiased standard deviation. The solutions seem to be using the biased standard deviation, so I'll create a custom function for that.*)
BiasedStandardDeviation[data_] :=
With[
{mean = Mean@data},
Sqrt[Total[(# - mean)^2 & /@ data]/Length[data]]
]
(*Mathematica's FoldPair functionality will work well with this if we provide a properly defined function to fold with.*)
DemingRule[1][funnelPosition_, diff_] := {funnelPosition + diff, 0};
DemingRule[2][funnelPosition_, diff_] := {funnelPosition + diff, -diff};
DemingRule[3][funnelPosition_, diff_] := {funnelPosition + diff, -funnelPosition - diff};
DemingRule[4][funnelPosition_, diff_] := {funnelPosition + diff, funnelPosition + diff};
(*The core implementation.*)
MarblePositions[rule_][diffs_] := FoldPairList[DemingRule[rule], 0, diffs];
(*This is to help format the output.*)
Results[rule_, diffData_] :=
With[
{positions = MarblePositions[rule][diffData]},
StringForm["Rule `1`\nmean: `2`\nstd dev: `3`", rule, Mean[positions], BiasedStandardDeviation[positions]]
];
TableForm[Results[#, Transpose[{dxs, dys}]] & /@ Range[4], TableSpacing -> 5]

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Task/Demings-funnel/Mathematica/demings-funnel-2.math Normal file
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RadiusDistribution = NormalDistribution[0, 1];
AngleDistribution = UniformDistribution[{0, Pi}];
(*Mathematica has built in transformation functions, but this seems clearer given the way the instructions were written.*)
ToCartesian[{r_, a_}] := ToCartesian[{Abs@r, a - Pi}] /; Negative[r];
ToCartesian[{r_, a_}] := FromPolarCoordinates[{r, a}];
newData =
ToCartesian /@
Transpose[{RandomVariate[RadiusDistribution, 100],
RandomVariate[AngleDistribution, 100]}];
TableForm[Results[#, newData] & /@ Range[4], TableSpacing -> 5]

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ListPlot[MarblePositions[#][Transpose[{dxs,dys}]]&/@Range[4],PlotLegends->PointLegend[{1,2,3,4}],AspectRatio->Automatic,ImageSize->600]

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Task/Demings-funnel/Nim/demings-funnel.nim Normal file
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import stats, strformat
type Rule = proc(x, y: float): float
const Dxs = [-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087]
const Dys = [ 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032]
func funnel(a: openArray[float]; rule: Rule): seq[float] =
var x = 0.0
result.setlen(a.len)
for i, val in a:
result[i] = x + val
x = rule(x, val)
proc experiment(label: string; r: Rule) =
let rxs = funnel(Dxs, r)
let rys = funnel(Dys, r)
echo label
echo fmt"Mean x, y : {rxs.mean:7.4f} {rys.mean:7.4f}"
echo fmt"Std dev x, y : {rxs.standardDeviation:7.4f} {rys.standardDeviation:7.4f}"
echo ""
experiment("Rule 1", proc(z, dz: float): float = 0.0)
experiment("Rule 2", proc(z, dz: float): float = -dz)
experiment("Rule 3", proc(z, dz: float): float = -(z + dz))
experiment("Rule 4", proc(z, dz: float): float = z + dz)

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Task/Demings-funnel/PARI-GP/demings-funnel.parigp Normal file
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drop(drops, rule, rnd)={
my(v=vector(drops),target=0);
v[1]=rule(target, 0);
for(i=2,drops,
target=rule(target, v[i-1]);
v[i]=rnd(n)+target
);
v
};
R=[-.533-.136*I,.27-.717*I,.859-.459*I,-.043+.225*I,-.205-1.39*I,-.127-.385*I,-.071-.121*I,.275+.395*I,1.25-.490*I,-.231+.682*I,-.401+.0650*I,.269-.242*I,.491+.288*I,.951-.658*I,1.15-.459*I,.001,-.382-.426*I,.161-.205*I,.915+.765*I,2.08+2.19*I,-2.34+.742*I,.034+.0100*I,-.126-.0890*I,.014-.208*I,.709-.585*I,.129-.633*I,-1.09+.444*I,-.483+.351*I,-1.19+1.09*I,.02-.199*I,-.051-.701*I,.047-.0960*I,-.095+.0250*I,.695+.868*I,.34-1.05*I,-.182-.157*I,.287-.216*I,.213-.162*I,-.423-.249*I,-.021+.00700*I,-0.134-.00900*I,1.8-.508*I,.021+.790*I,-1.1-.723*I,-.361-.881*I,1.64+.508*I,-1.13-.393*I,1.32+.226*I,.201-.710*I,.034-.0380*I,.097+.217*I,-.17-.831*I,.054-.480*I,-.553-.407*I,-.024-.447*I,-.181+.295*I,-.7-1.13*I,-.361-.380*I,-.789-.549*I,.279+.445*I,-.174+.0460*I,-.009-.428*I,-.323+.0740*I,-.658-.217*I,.348+.822*I,-.528-.491*I,.881-1.35*I,.021+.141*I,-.853-1.23*I,.157+.0440*I,.648-.0790*I,1.77-.219*I,-1.04-.698*I,.051-.275*I,.021-.0560*I,.247-.0310*I,-.31-.421*I,.171-.0640*I,-.721*I,.106-.104*I,.024+.729*I,-.386-.650*I,.962+1.10*I,.765-.154*I,-.125+1.72*I,-.289-.0510*I,.521+.385*I,.017-.477*I,.281-1.54*I,-.749+.901*I,-.149-.939*I,-2.44+.411*I,-.909-.341*I,.394+.411*I,-.113-.106*I,-.598-.224*I,.443+.947*I,-.521+1.42*I,-.799+.542*I,.087+1.03*I];
rule1(target, result)=0;
rule2(target, result)=target-result;
rule3(target, result)=-result;
rule4(target, result)=result;
mean(v)=sum(i=1,#v,v[i])/#v;
stdev(v,mu=mean(v))=sqrt(sum(i=1,#v,(v[i]-mu)^2)/#v);
main()={
my(V);
V=apply(f->drop(100,f,n->R[n]), [rule1, rule2, rule3, rule4]);
for(i=1,4,
print("Method #"i);
print("Means: ", mean(real(V[i])), "\t", mean(imag(V[i])));
print("StDev: ", stdev(real(V[i])), "\t", stdev(imag(V[i])));
print()
)
}

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Task/Demings-funnel/Perl/demings-funnel.pl Normal file
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@dx = qw<
-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275
1.251 -0.231 -0.401 0.269 0.491 0.951 1.150 0.001
-0.382 0.161 0.915 2.080 -2.337 0.034 -0.126 0.014
0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051 0.047
-0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021
-0.134 1.798 0.021 -1.099 -0.361 1.636 -1.134 1.315
0.201 0.034 0.097 -0.170 0.054 -0.553 -0.024 -0.181
-0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323 -0.658
0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774
-1.043 0.051 0.021 0.247 -0.310 0.171 0.000 0.106
0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521 0.017
0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
0.443 -0.521 -0.799 0.087>;
@dy = qw<
0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395
0.490 -0.682 -0.065 0.242 -0.288 0.658 0.459 0.000
0.426 0.205 -0.765 -2.188 -0.742 -0.010 0.089 0.208
0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096
-0.025 -0.868 1.051 0.157 0.216 0.162 0.249 -0.007
0.009 0.508 -0.790 0.723 0.881 -0.508 0.393 -0.226
0.710 0.038 -0.217 0.831 0.480 0.407 0.447 -0.295
1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217
-0.822 0.491 1.347 -0.141 1.230 -0.044 0.079 0.219
0.698 0.275 0.056 0.031 0.421 0.064 0.721 0.104
-0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477
1.537 -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224
-0.947 -1.424 -0.542 -1.032>;
sub mean { my $s; $s += $_ for @_; $s / @_ }
sub stddev { sqrt( mean(map { $_**2 } @_) - mean(@_)**2) }
@rules = (
sub { 0 },
sub { -$_[1] },
sub { -$_[0] - $_[1] },
sub { $_[0] + $_[1] }
);
for (@rules) {
print "Rule " . ++$cnt . "\n";
my @ddx; my $tx = 0;
for my $x (@dx) { push @ddx, $tx + $x; $tx = &$_($tx, $x) }
my @ddy; my $ty = 0;
for my $y (@dy) { push @ddy, $ty + $y; $ty = &$_($ty, $y) }
printf "Mean x, y : %7.4f %7.4f\n", mean(@ddx), mean(@ddy);
printf "Std dev x, y : %7.4f %7.4f\n", stddev(@ddx), stddev(@ddy);
}

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Task/Demings-funnel/Phix/demings-funnel.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">funnel</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">dxs</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">rule</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rxs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dxs</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dxs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rxs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rxs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">rule</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">dx</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dx</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">rxs</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">xs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">)/</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">stddev</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">xs</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))/</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">experiment</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">dxs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dys</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rxs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">funnel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dxs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">rys</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">funnel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dys</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Mean x, y : %7.4f, %7.4f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rxs</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rys</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Std dev x, y : %7.4f, %7.4f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">stddev</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rxs</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">stddev</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rys</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">dxs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">0.533</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.270</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.859</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.043</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.205</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.127</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.071</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.275</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.251</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.231</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.401</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.269</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.491</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.951</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.150</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.001</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.382</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.161</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.915</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.080</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2.337</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.034</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.126</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.014</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.709</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.129</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.093</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.483</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.193</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.020</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.051</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.047</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.095</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.695</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.340</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.182</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.287</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.213</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.423</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.021</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.134</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.798</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.021</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.099</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.361</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.636</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.134</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.315</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.201</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.034</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.097</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.170</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.054</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.553</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.024</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.181</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.700</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.361</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.789</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.279</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.174</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.009</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.323</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.658</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.348</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.528</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.881</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.021</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.853</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.157</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.648</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.774</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">1.043</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.051</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.021</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.247</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.310</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.171</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.106</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.024</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.386</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.962</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.765</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.125</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.289</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.521</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.017</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.281</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.749</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.149</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2.436</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.909</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.394</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.113</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.598</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.443</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.521</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.799</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.087</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">dys</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">0.136</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.717</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.459</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.225</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.392</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.385</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.121</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.395</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.490</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.682</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.065</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.242</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.288</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.658</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.459</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.426</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.205</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.765</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2.188</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.742</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.010</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.089</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.208</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.585</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.633</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.444</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.351</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.087</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.199</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.701</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.096</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.025</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.868</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.051</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.157</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.216</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.162</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.249</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.007</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.009</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.508</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.790</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.723</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.881</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.508</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.393</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.226</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.710</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.038</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.217</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.831</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.480</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.407</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.447</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.295</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.126</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.380</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.549</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.445</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.046</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.428</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.074</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.217</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.822</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.491</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.347</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.141</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.230</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.044</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.079</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.219</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.698</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.275</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.056</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.031</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.421</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.064</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.721</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.104</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.729</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.650</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.103</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.154</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.720</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.051</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.385</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.477</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.537</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.901</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.939</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.411</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.341</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.411</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.106</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.224</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.947</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.424</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.542</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.032</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">experiment</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dxs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dys</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--

50
Task/Demings-funnel/Python/demings-funnel-1.py Normal file
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import math
dxs = [-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275, 1.251,
-0.231, -0.401, 0.269, 0.491, 0.951, 1.15, 0.001, -0.382, 0.161, 0.915,
2.08, -2.337, 0.034, -0.126, 0.014, 0.709, 0.129, -1.093, -0.483, -1.193,
0.02, -0.051, 0.047, -0.095, 0.695, 0.34, -0.182, 0.287, 0.213, -0.423,
-0.021, -0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315, 0.201,
0.034, 0.097, -0.17, 0.054, -0.553, -0.024, -0.181, -0.7, -0.361, -0.789,
0.279, -0.174, -0.009, -0.323, -0.658, 0.348, -0.528, 0.881, 0.021, -0.853,
0.157, 0.648, 1.774, -1.043, 0.051, 0.021, 0.247, -0.31, 0.171, 0.0, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017, 0.281, -0.749,
-0.149, -2.436, -0.909, 0.394, -0.113, -0.598, 0.443, -0.521, -0.799,
0.087]
dys = [0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395, 0.49, -0.682,
-0.065, 0.242, -0.288, 0.658, 0.459, 0.0, 0.426, 0.205, -0.765, -2.188,
-0.742, -0.01, 0.089, 0.208, 0.585, 0.633, -0.444, -0.351, -1.087, 0.199,
0.701, 0.096, -0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.79, 0.723, 0.881, -0.508, 0.393, -0.226, 0.71, 0.038,
-0.217, 0.831, 0.48, 0.407, 0.447, -0.295, 1.126, 0.38, 0.549, -0.445,
-0.046, 0.428, -0.074, 0.217, -0.822, 0.491, 1.347, -0.141, 1.23, -0.044,
0.079, 0.219, 0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.65, -1.103, 0.154, -1.72, 0.051, -0.385, 0.477, 1.537, -0.901,
0.939, -0.411, 0.341, -0.411, 0.106, 0.224, -0.947, -1.424, -0.542, -1.032]
def funnel(dxs, rule):
x, rxs = 0, []
for dx in dxs:
rxs.append(x + dx)
x = rule(x, dx)
return rxs
def mean(xs): return sum(xs) / len(xs)
def stddev(xs):
m = mean(xs)
return math.sqrt(sum((x-m)**2 for x in xs) / len(xs))
def experiment(label, rule):
rxs, rys = funnel(dxs, rule), funnel(dys, rule)
print label
print 'Mean x, y : %.4f, %.4f' % (mean(rxs), mean(rys))
print 'Std dev x, y : %.4f, %.4f' % (stddev(rxs), stddev(rys))
print
experiment('Rule 1:', lambda z, dz: 0)
experiment('Rule 2:', lambda z, dz: -dz)
experiment('Rule 3:', lambda z, dz: -(z+dz))
experiment('Rule 4:', lambda z, dz: z+dz)

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Task/Demings-funnel/Python/demings-funnel-2.py Normal file
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from random import gauss
from math import sqrt
from pprint import pprint as pp
NMAX=50
def statscreator():
sum_ = sum2 = n = 0
def stats(x):
nonlocal sum_, sum2, n
sum_ += x
sum2 += x*x
n += 1.0
return sum_/n, sqrt(sum2/n - sum_*sum_/n/n)
return stats
def drop(target, sigma=1.0):
'Drop ball at target'
return gauss(target, sigma)
def deming(rule, nmax=NMAX):
''' Simulate Demings funnel in 1D. '''
stats = statscreator()
target = 0
for i in range(nmax):
value = drop(target)
mean, sdev = stats(value)
target = rule(target, value)
if i == nmax - 1:
return mean, sdev
def d1(target, value):
''' Keep Funnel over target. '''
return target
def d2(target, value):
''' The new target starts at the center, 0,0 then is adjusted to
be the previous target _minus_ the offset of the new drop from the
previous target. '''
return -value # - (target - (target - value)) = - value
def d3(target, value):
''' The new target starts at the center, 0,0 then is adjusted to
be the previous target _minus_ the offset of the new drop from the
center, 0.0. '''
return target - value
def d4(target, value):
''' (Dumb). The new target is where it last dropped. '''
return value
def printit(rule, trials=5):
print('\nDeming simulation. %i trials using rule %s:\n %s'
% (trials, rule.__name__.upper(), rule.__doc__))
for i in range(trials):
print(' Mean: %7.3f, Sdev: %7.3f' % deming(rule))
if __name__ == '__main__':
rcomments = [ (d1, 'Should have smallest deviations ~1.0, and be centered on 0.0'),
(d2, 'Should be centred on 0.0 with larger deviations than D1'),
(d3, 'Should be centred on 0.0 with larger deviations than D1'),
(d4, 'Center wanders all over the place, with deviations to match!'),
]
for rule, comment in rcomments:
printit(rule)
print(' %s\n' % comment)

51
Task/Demings-funnel/Racket/demings-funnel.rkt Normal file
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#lang racket
(require math/distributions math/statistics plot)
(define dxs '(-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275 1.251 -0.231
-0.401 0.269 0.491 0.951 1.150 0.001 -0.382 0.161 0.915 2.080 -2.337
0.034 -0.126 0.014 0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051
0.047 -0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021 -0.134 1.798
0.021 -1.099 -0.361 1.636 -1.134 1.315 0.201 0.034 0.097 -0.170 0.054
-0.553 -0.024 -0.181 -0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323
-0.658 0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774 -1.043 0.051
0.021 0.247 -0.310 0.171 0.000 0.106 0.024 -0.386 0.962 0.765 -0.125
-0.289 0.521 0.017 0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
0.443 -0.521 -0.799 0.087))
(define dys '(0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395 0.490 -0.682 -0.065
0.242 -0.288 0.658 0.459 0.000 0.426 0.205 -0.765 -2.188 -0.742 -0.010
0.089 0.208 0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096 -0.025
-0.868 1.051 0.157 0.216 0.162 0.249 -0.007 0.009 0.508 -0.790 0.723
0.881 -0.508 0.393 -0.226 0.710 0.038 -0.217 0.831 0.480 0.407 0.447
-0.295 1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217 -0.822 0.491
1.347 -0.141 1.230 -0.044 0.079 0.219 0.698 0.275 0.056 0.031 0.421 0.064
0.721 0.104 -0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477 1.537
-0.901 0.939 -0.411 0.341 -0.411 0.106 0.224 -0.947 -1.424 -0.542 -1.032))
;(define radii (map abs (sample (normal-dist 0 1) 100)))
;(define angles (sample (uniform-dist (- pi) pi) 100))
;(define dxs (map (λ (r theta) (* r (cos theta))) radii angles))
;(define dys (map (λ (r theta) (* r (sin theta))) radii angles))
(define (funnel dxs rule)
(let ([x 0])
(for/fold ([rxs null])
([dx dxs])
(let ([rx (+ x dx)])
(set! x (rule x dx))
(cons rx rxs)))))
(define (experiment label rule)
(define (p s) (real->decimal-string s 4))
(let ([rxs (funnel dxs rule)]
[rys (funnel dys rule)])
(displayln label)
(printf "Mean x, y : ~a, ~a\n" (p (mean rxs)) (p (mean rys)))
(printf "Std dev x, y: ~a, ~a\n\n" (p (stddev rxs)) (p (stddev rys)))
#;(plot (points (map vector rxs rys)
#:x-min -15 #:x-max 15 #:y-min -15 #:y-max 15))))
(experiment "Rule 1:" (λ (z dz) 0))
(experiment "Rule 2:" (λ (z dz) (- dz)))
(experiment "Rule 3:" (λ (z dz) (- (+ z dz))))
(experiment "Rule 4:" (λ (z dz) (+ z dz)))

53
Task/Demings-funnel/Raku/demings-funnel.raku Normal file
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sub mean { @_ R/ [+] @_ }
sub stddev {
# <(x - <x>)²> = <x²> - <x>²
sqrt( mean(@_ »**» 2) - mean(@_)**2 )
}
constant @dz = <
-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275
1.251 -0.231 -0.401 0.269 0.491 0.951 1.150 0.001
-0.382 0.161 0.915 2.080 -2.337 0.034 -0.126 0.014
0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051 0.047
-0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021
-0.134 1.798 0.021 -1.099 -0.361 1.636 -1.134 1.315
0.201 0.034 0.097 -0.170 0.054 -0.553 -0.024 -0.181
-0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323 -0.658
0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774
-1.043 0.051 0.021 0.247 -0.310 0.171 0.000 0.106
0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521 0.017
0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
0.443 -0.521 -0.799 0.087
> Z+ (1i X* <
0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395
0.490 -0.682 -0.065 0.242 -0.288 0.658 0.459 0.000
0.426 0.205 -0.765 -2.188 -0.742 -0.010 0.089 0.208
0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096
-0.025 -0.868 1.051 0.157 0.216 0.162 0.249 -0.007
0.009 0.508 -0.790 0.723 0.881 -0.508 0.393 -0.226
0.710 0.038 -0.217 0.831 0.480 0.407 0.447 -0.295
1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217
-0.822 0.491 1.347 -0.141 1.230 -0.044 0.079 0.219
0.698 0.275 0.056 0.031 0.421 0.064 0.721 0.104
-0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477
1.537 -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224
-0.947 -1.424 -0.542 -1.032
>);
constant @rule =
-> \z, \dz { 0 },
-> \z, \dz { -dz },
-> \z, \dz { -z - dz },
-> \z, \dz { z + dz },
;
for @rule {
say "Rule $(++$):";
my $target = 0i;
my @z = gather for @dz -> $dz {
take $target + $dz;
$target = .($target, $dz)
}
printf "Mean x, y : %7.4f %7.4f\n", mean(@z».re), mean(@z».im);
printf "Std dev x, y : %7.4f %7.4f\n", stddev(@z».re), stddev(@z».im);
}

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Task/Demings-funnel/Ruby/demings-funnel.rb Normal file
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def funnel(dxs, &rule)
x, rxs = 0, []
for dx in dxs
rxs << (x + dx)
x = rule[x, dx]
end
rxs
end
def mean(xs) xs.inject(:+) / xs.size end
def stddev(xs)
m = mean(xs)
Math.sqrt(xs.inject(0.0){|sum,x| sum + (x-m)**2} / xs.size)
end
def experiment(label, dxs, dys, &rule)
rxs, rys = funnel(dxs, &rule), funnel(dys, &rule)
puts label
puts 'Mean x, y : %7.4f, %7.4f' % [mean(rxs), mean(rys)]
puts 'Std dev x, y : %7.4f, %7.4f' % [stddev(rxs), stddev(rys)]
puts
end
dxs = [ -0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087]
dys = [ 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032]
experiment('Rule 1:', dxs, dys) {|z, dz| 0}
experiment('Rule 2:', dxs, dys) {|z, dz| -dz}
experiment('Rule 3:', dxs, dys) {|z, dz| -(z+dz)}
experiment('Rule 4:', dxs, dys) {|z, dz| z+dz}

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Task/Demings-funnel/Sidef/demings-funnel.sidef Normal file
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func x̄(a) {
a.sum / a.len
}
func σ(a) {
sqrt(x̄(a.map{.**2}) - x̄(a)**2)
}
const Δ = (%n<
-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275
1.251 -0.231 -0.401 0.269 0.491 0.951 1.150 0.001
-0.382 0.161 0.915 2.080 -2.337 0.034 -0.126 0.014
0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051 0.047
-0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021
-0.134 1.798 0.021 -1.099 -0.361 1.636 -1.134 1.315
0.201 0.034 0.097 -0.170 0.054 -0.553 -0.024 -0.181
-0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323 -0.658
0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774
-1.043 0.051 0.021 0.247 -0.310 0.171 0.000 0.106
0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521 0.017
0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
0.443 -0.521 -0.799 0.087
> ~Z+ %n<
0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395
0.490 -0.682 -0.065 0.242 -0.288 0.658 0.459 0.000
0.426 0.205 -0.765 -2.188 -0.742 -0.010 0.089 0.208
0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096
-0.025 -0.868 1.051 0.157 0.216 0.162 0.249 -0.007
0.009 0.508 -0.790 0.723 0.881 -0.508 0.393 -0.226
0.710 0.038 -0.217 0.831 0.480 0.407 0.447 -0.295
1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217
-0.822 0.491 1.347 -0.141 1.230 -0.044 0.079 0.219
0.698 0.275 0.056 0.031 0.421 0.064 0.721 0.104
-0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477
1.537 -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224
-0.947 -1.424 -0.542 -1.032
>.map{ .i })
const rules = [
{ 0 },
{|_,dz| -dz },
{|z,dz| -z - dz },
{|z,dz| z + dz },
]
for i,v in (rules.kv) {
say "Rule #{i+1}:"
var target = 0
var z = gather {
Δ.each { |d|
take(target + d)
target = v.run(target, d)
}
}
printf("Mean x, y : %.4f %.4f\n", x̄(z.map{.re}), x̄(z.map{.im}))
printf("Std dev x, y : %.4f %.4f\n", σ(z.map{.re}), σ(z.map{.im}))
}

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import Foundation
let dxs = [
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087
]
let dys = [
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032
]
extension Collection where Element: FloatingPoint {
@inlinable
public func mean() -> Element {
return reduce(0, +) / Element(count)
}
@inlinable
public func stdDev() -> Element {
let m = mean()
return map({ ($0 - m) * ($0 - m) }).mean().squareRoot()
}
}
typealias Rule = (Double, Double) -> Double
func funnel(_ arr: [Double], rule: Rule) -> [Double] {
var x = 0.0
var res = [Double](repeating: 0, count: arr.count)
for (i, d) in arr.enumerated() {
res[i] = x + d
x = rule(x, d)
}
return res
}
func experiment(label: String, rule: Rule) {
let rxs = funnel(dxs, rule: rule)
let rys = funnel(dys, rule: rule)
print("\(label)\t: x y")
print("Mean\t:\(String(format: "%7.4f, %7.4f", rxs.mean(), rys.mean()))")
print("Std Dev\t:\(String(format: "%7.4f, %7.4f", rxs.stdDev(), rys.stdDev()))")
print()
}
experiment(label: "Rule 1", rule: {_, _ in 0 })
experiment(label: "Rule 2", rule: {_, dz in -dz })
experiment(label: "Rule 3", rule: {z, dz in -(z + dz) })
experiment(label: "Rule 4", rule: {z, dz in z + dz })

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Task/Demings-funnel/Tcl/demings-funnel-1.tcl Normal file
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package require Tcl 8.6
namespace path {tcl::mathop tcl::mathfunc}
proc funnel {items rule} {
set x 0.0
set result {}
foreach item $items {
lappend result [+ $x $item]
set x [apply $rule $x $item]
}
return $result
}
proc mean {items} {
/ [+ {*}$items] [double [llength $items]]
}
proc stddev {items} {
set m [mean $items]
sqrt [mean [lmap x $items {** [- $x $m] 2}]]
}
proc experiment {label dxs dys rule} {
set rxs [funnel $dxs $rule]
set rys [funnel $dys $rule]
puts $label
puts [format "Mean x, y : %7.4f, %7.4f" [mean $rxs] [mean $rys]]
puts [format "Std dev x, y : %7.4f, %7.4f" [stddev $rxs] [stddev $rys]]
puts ""
}
set dxs {
-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275 1.251 -0.231 -0.401
0.269 0.491 0.951 1.150 0.001 -0.382 0.161 0.915 2.080 -2.337 0.034
-0.126 0.014 0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051 0.047 -0.095
0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021 -0.134 1.798 0.021 -1.099
-0.361 1.636 -1.134 1.315 0.201 0.034 0.097 -0.170 0.054 -0.553 -0.024
-0.181 -0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323 -0.658 0.348
-0.528 0.881 0.021 -0.853 0.157 0.648 1.774 -1.043 0.051 0.021 0.247
-0.310 0.171 0.000 0.106 0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521
0.017 0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598 0.443 -0.521
-0.799 0.087
}
set dys {
0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395 0.490 -0.682 -0.065
0.242 -0.288 0.658 0.459 0.000 0.426 0.205 -0.765 -2.188 -0.742 -0.010
0.089 0.208 0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096 -0.025
-0.868 1.051 0.157 0.216 0.162 0.249 -0.007 0.009 0.508 -0.790 0.723
0.881 -0.508 0.393 -0.226 0.710 0.038 -0.217 0.831 0.480 0.407 0.447
-0.295 1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217 -0.822 0.491
1.347 -0.141 1.230 -0.044 0.079 0.219 0.698 0.275 0.056 0.031 0.421 0.064
0.721 0.104 -0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477 1.537
-0.901 0.939 -0.411 0.341 -0.411 0.106 0.224 -0.947 -1.424 -0.542 -1.032
}
puts "USING STANDARD DATA"
experiment "Rule 1:" $dxs $dys {{z dz} {expr {0}}}
experiment "Rule 2:" $dxs $dys {{z dz} {expr {-$dz}}}
experiment "Rule 3:" $dxs $dys {{z dz} {expr {-($z+$dz)}}}
experiment "Rule 4:" $dxs $dys {{z dz} {expr {$z+$dz}}}

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Task/Demings-funnel/Tcl/demings-funnel-2.tcl Normal file
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package require math::constants
package require simulation::random
math::constants::constants degtorad
set rng(radius) [simulation::random::prng_Normal 0.0 1.0]
set rng(angle) [simulation::random::prng_Uniform 0.0 360.0]
set dxs [set dys {}]
for {set i 0} {$i < 500} {incr i} {
set r [$rng(radius)]
set theta [expr {[$rng(angle)] * $degtorad}]
lappend dxs [expr {$r * cos($theta)}]
lappend dys [expr {$r * sin($theta)}]
}
puts "USING RANDOM DATA"
experiment "Rule 1:" $dxs $dys {{z dz} {expr {0}}}
experiment "Rule 2:" $dxs $dys {{z dz} {expr {-$dz}}}
experiment "Rule 3:" $dxs $dys {{z dz} {expr {-($z+$dz)}}}
experiment "Rule 4:" $dxs $dys {{z dz} {expr {$z+$dz}}}

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Task/Demings-funnel/V-(Vlang)/demings-funnel.v Normal file
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import math
type Rule = fn(f64, f64) f64
const (
dxs = [
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087,
]
dys = [
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032,
]
)
fn funnel(fa []f64, r Rule) []f64 {
mut x := 0.0
mut result := []f64{len: fa.len}
for i, f in fa {
result[i] = x + f
x = r(x, f)
}
return result
}
fn mean(fa []f64) f64 {
mut sum := 0.0
for f in fa {
sum += f
}
return sum / f64(fa.len)
}
fn std_dev(fa []f64) f64 {
m := mean(fa)
mut sum := 0.0
for f in fa {
sum += (f - m) * (f - m)
}
return math.sqrt(sum / f64(fa.len))
}
fn experiment(label string, r Rule) {
rxs := funnel(dxs, r)
rys := funnel(dys, r)
println("$label : x y")
println("Mean : ${mean(rxs):7.4f}, ${mean(rys):7.4f}")
println("Std Dev : ${std_dev(rxs):7.4f}, ${std_dev(rys):7.4f}")
println('')
}
fn main() {
experiment("Rule 1", fn(_ f64, _ f64) f64 {
return 0.0
})
experiment("Rule 2", fn(_ f64, dz f64) f64 {
return -dz
})
experiment("Rule 3", fn(z f64, dz f64) f64 {
return -(z + dz)
})
experiment("Rule 4", fn(z f64, dz f64) f64 {
return z + dz
})
}

59
Task/Demings-funnel/Wren/demings-funnel.wren Normal file
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import "/math" for Nums
import "/fmt" for Fmt
var dxs = [
-0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087
]
var dys = [
0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032
]
var funnel = Fn.new { |fa, r|
var x = 0
var res = List.filled(fa.count, 0)
for (i in 0...fa.count) {
var f = fa[i]
res[i] = x + f
x = r.call(x, f)
}
return res
}
var experiment = Fn.new { |label, r|
var rxs = funnel.call(dxs, r)
var rys = funnel.call(dys, r)
System.print("%(label) : x y")
System.print("Mean : %(Fmt.f(7, Nums.mean(rxs), 4)), %(Fmt.f(7, Nums.mean(rys), 4))")
System.print("Std Dev : %(Fmt.f(7, Nums.popStdDev(rxs), 4)), %(Fmt.f(7, Nums.popStdDev(rys), 4))")
System.print()
}
experiment.call("Rule 1") { |z, dz| 0 }
experiment.call("Rule 2") { |z, dz| -dz }
experiment.call("Rule 3") { |z, dz| -(z + dz) }
experiment.call("Rule 4") { |z, dz| z + dz }

88
Task/Demings-funnel/XPL0/demings-funnel.xpl0 Normal file
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include xpllib; \for Print
func real Mean(Array, Size);
real Array; int Size;
real Sum;
int I;
[Sum:= 0.0;
for I:= 0 to Size-1 do
Sum:= Sum + Array(I);
return Sum / float(Size);
];
func real StdDev(Array, Size);
real Array; int Size;
real M, Sum;
int I;
[M:= Mean(Array, Size);
Sum:= 0.0;
for I:= 0 to Size-1 do
Sum:= Sum + (Array(I)-M) * (Array(I)-M);
return sqrt(Sum / float(Size));
];
func real Funnel(Array, Size, Rule);
real Array; int Size, Rule;
real Posn, Result, Fall;
int AddrResult, I;
def SizeOfReal = 8; \bytes
[AddrResult:= addr Result;
AddrResult(0):= MAlloc(Size*SizeOfReal);
AddrResult(1):= 0; \for safety
Posn:= 0.0;
for I:= 0 to Size-1 do
[Fall:= Array(I);
Result(I):= Posn + Fall;
case Rule of
1: [];
2: Posn:= -Fall;
3: Posn:= -(Posn+Fall);
4: Posn:= Posn+Fall
other [];
];
return Result;
];
func Experiment(Rule);
int Rule;
real DXs, DYs, RXs, RYs;
def Size = 100;
[
DXs:= [ -0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087 ];
DYs:= [ 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032 ];
RXs:= Funnel(DXs, Size, Rule);
RYs:= Funnel(DYs, Size, Rule);
Print("Rule %d : X Y\n", Rule);
Print("Mean : %3.4f, %3.4f\n", Mean(RXs, Size), Mean(RYs, Size));
Print("Std Dev : %3.4f, %3.4f\n", StdDev(RXs, Size), StdDev(RYs, Size));
CrLf(0);
];
int R;
for R:= 1 to 4 do Experiment(R)

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Task/Demings-funnel/Zkl/demings-funnel-1.zkl Normal file
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fcn funnel(dxs, rule){
x:=0.0; rxs:=L();
foreach dx in (dxs){
rxs.append(x + dx);
x = rule(x,dx);
}
rxs
}
fcn mean(xs){ xs.sum(0.0)/xs.len() }
fcn stddev(xs){
m:=mean(xs);
(xs.reduce('wrap(sum,x){ sum + (x-m)*(x-m) },0.0)/xs.len()).sqrt();
}
fcn experiment(label,dxs,dys,rule){
rxs:=funnel(dxs,rule); rys:=funnel(dys,rule);
label.println();
"Mean x, y : %7.4f, %7.4f".fmt(mean(rxs), mean(rys)) .println();
"Std dev x, y : %7.4f, %7.4f".fmt(stddev(rxs),stddev(rys)).println();
println();
}

32
Task/Demings-funnel/Zkl/demings-funnel-2.zkl Normal file
View file

@ -0,0 +1,32 @@
dxs:=T( -0.533, 0.270, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,
-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,
0.709, 0.129, -1.093, -0.483, -1.193, 0.020, -0.051, 0.047,
-0.095, 0.695, 0.340, -0.182, 0.287, 0.213, -0.423, -0.021,
-0.134, 1.798, 0.021, -1.099, -0.361, 1.636, -1.134, 1.315,
0.201, 0.034, 0.097, -0.170, 0.054, -0.553, -0.024, -0.181,
-0.700, -0.361, -0.789, 0.279, -0.174, -0.009, -0.323, -0.658,
0.348, -0.528, 0.881, 0.021, -0.853, 0.157, 0.648, 1.774,
-1.043, 0.051, 0.021, 0.247, -0.310, 0.171, 0.000, 0.106,
0.024, -0.386, 0.962, 0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087);
dys:=T( 0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.490, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0.000,
0.426, 0.205, -0.765, -2.188, -0.742, -0.010, 0.089, 0.208,
0.585, 0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096,
-0.025, -0.868, 1.051, 0.157, 0.216, 0.162, 0.249, -0.007,
0.009, 0.508, -0.790, 0.723, 0.881, -0.508, 0.393, -0.226,
0.710, 0.038, -0.217, 0.831, 0.480, 0.407, 0.447, -0.295,
1.126, 0.380, 0.549, -0.445, -0.046, 0.428, -0.074, 0.217,
-0.822, 0.491, 1.347, -0.141, 1.230, -0.044, 0.079, 0.219,
0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721, 0.104,
-0.729, 0.650, -1.103, 0.154, -1.720, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106, 0.224,
-0.947, -1.424, -0.542, -1.032);
experiment("Rule 1:", dxs, dys, fcn(z,dz){ 0.0 });
experiment("Rule 2:", dxs, dys, fcn(z,dz){ -dz });
experiment("Rule 3:", dxs, dys, fcn(z,dz){ -(z+dz) });
experiment("Rule 4:", dxs, dys, fcn(z,dz){ z+dz });