Deming's funnel
You are encouraged to solve this task according to the task description, using any language you may know.
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 explanation and interpretation
- Video demonstration of the funnel experiment at the Mayo Clinic.
11l
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)- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
Ada
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;
ALGOL 68
Note, the source of the RC ALGOL 68 rows library (rows.incl.a68) containing the AVERAGE and STANDARDDEVIATION operators is on a separate page on Rosetta Code - see the above link.
BEGIN # Deming's funnel - translated from Python #
PR read "rows.incl.a68" PR # include row (array) utilities #
PROC funnel = ( INT rule, []REAL dxs )[]REAL:
BEGIN
[ LWB dxs : UPB dxs ]REAL rvs; REAL v := 0;
FOR dx pos FROM LWB dxs TO UPB dxs DO
REAL dx = dxs[ dx pos ];
rvs[ dx pos ] := v + dx;
IF rule = 1 THEN
v := 0
ELIF rule = 2 THEN
v := - dx
ELIF rule = 3 THEN
v := - ( v + dx )
ELSE
v +:= dx
FI
OD;
rvs
END # funnel # ;
PROC experiment = ( INT rule, []REAL dxs, dys )VOID:
BEGIN
[]REAL rxs = funnel( rule, dxs );
[]REAL rys = funnel( rule, dys );
print( ( "Rule ", whole( rule, - 4 ), ": " ) );
print( ( "Mean x, y : ", fixed( AVERAGE rxs, -8, 4 ) ) );
print( ( " ", fixed( AVERAGE rys, -8, 4 ), newline ) );
print( ( " " ) );
print( ( "Std dev x, y : ", fixed( STANDARDDEVIATION rxs, -8, 4 ) ) );
print( ( " ", fixed( STANDARDDEVIATION rys, -8, 4 ), newline ) );
print( ( newline ) )
END # experiment # ;
BEGIN
[]REAL 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
);
[]REAL 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
);
experiment( 1, dxs, dys );
experiment( 2, dxs, dys );
experiment( 3, dxs, dys );
experiment( 4, dxs, dys )
END
END- Output:
Rule 1: Mean x, y : 0.0004 0.0702
Std dev x, y : 0.7153 0.6462
Rule 2: Mean x, y : 0.0009 -0.0103
Std dev x, y : 1.0371 0.8999
Rule 3: Mean x, y : 0.0439 -0.0063
Std dev x, y : 7.9871 4.7784
Rule 4: Mean x, y : 3.1341 5.4210
Std dev x, y : 1.5874 3.9304
Arturo
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]
- Output:
Rule 1 ============================== Mean x,y : 0.0004 0.0702 Std.dev x,y : 0.7153 0.6462 Rule 2 ============================== Mean x,y : 0.0009 -0.0103 Std.dev x,y : 1.0371 0.8999 Rule 3 ============================== Mean x,y : 0.0439 -0.0063 Std.dev x,y : 7.9871 4.7784 Rule 4 ============================== Mean x,y : 3.1341 5.4210 Std.dev x,y : 1.5874 3.9304
C#
using System;
using System.Linq;
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, Func<double, double, double> rule)
{
double[] resx = Funnel(dxs, rule);
double[] resy = Funnel(dys, rule);
Console.WriteLine(label);
Console.WriteLine($"Mean x, y: {Mean(resx):F4}, {Mean(resy):F4}");
Console.WriteLine($"Std dev x, y: {StdDev(resx):F4}, {StdDev(resy):F4}");
Console.WriteLine();
}
static double[] Funnel(double[] input, Func<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(x, input[i]);
result[i] = rx;
}
return result;
}
static double Mean(double[] xs)
{
return xs.Average();
}
static double StdDev(double[] xs)
{
double m = Mean(xs);
return Math.Sqrt(xs.Select(x => Math.Pow((x - m), 2)).Sum() / xs.Length);
}
}
- Output:
Rule 1: Mean x, y: 0.0004, 0.0702 Std dev x, y: 0.7153, 0.6462 Rule 2: Mean x, y: 0.0009, -0.0103 Std dev x, y: 1.0371, 0.8999 Rule 3: Mean x, y: 0.0439, -0.0063 Std dev x, y: 7.9871, 4.7784 Rule 4: Mean x, y: 3.1341, 5.4210 Std dev x, y: 1.5874, 3.9304
C++
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
double mean(const std::vector<double>& pseudo_random) {
double sum = 0.0;
for ( double item : pseudo_random ) {
sum += item;
}
return sum / pseudo_random.size();
}
double standard_deviation(const std::vector<double>& pseudo_random) {
const double average = mean(pseudo_random);
double sum_squares = 0.0;
for ( double item : pseudo_random ) {
sum_squares += item * item;
}
return sqrt(sum_squares / pseudo_random.size() - average * average);
}
std::vector<double> funnel(const std::vector<double>& pseudo_random,
const std::function<double(double, double)>& rule) {
double value = 0.0;
std::vector<double> result(pseudo_random.size(), 0);
for ( size_t i = 0; i < pseudo_random.size(); i++ ) {
const double result_value = value + pseudo_random[i];
value = rule(value, pseudo_random[i]);
result[i] = result_value;
}
return result;
}
void experiment(const std::string& label, const std::vector<double>& pseudo_random_xs,
const std::vector<double>& pseudo_random_ys, const std::function<double(double, double)>& rule) {
std::vector<double> result_x = funnel(pseudo_random_xs, rule);
std::vector<double> result_y = funnel(pseudo_random_ys, rule);
std::cout << label << std::endl;
std::cout << "-----------------------------------------" << std::endl;
std::cout << "Mean x, y" << std::setw(16) << ": " << std::fixed << std::setprecision(4)
<< mean(result_x) << ", " << mean(result_y) << std::endl;
std::cout << "Standard deviation x, y: " << standard_deviation(result_x) << ", "
<< standard_deviation(result_y) << std::endl;
std::cout << std::endl;
}
int main() {
const std::vector<double> pseudo_random_xs = { -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 std::vector<double> pseudo_random_ys = { 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:", pseudo_random_xs, pseudo_random_ys, [](double z, double dz) -> double { return 0.0; });
experiment("Rule 2:", pseudo_random_xs, pseudo_random_ys, [](double z, double dz) -> double { return -dz; });
experiment("Rule 3:", pseudo_random_xs, pseudo_random_ys, [](double z, double dz) -> double { return -(z + dz); });
experiment("Rule 4:", pseudo_random_xs, pseudo_random_ys, [](double z, double dz) -> double { return z + dz; });
}
- Output:
Rule 1: ----------------------------------------- Mean x, y : 0.0004, 0.0702 Standard deviation x, y: 0.7153, 0.6462 Rule 2: ----------------------------------------- Mean x, y : 0.0009, -0.0103 Standard deviation x, y: 1.0371, 0.8999 Rule 3: ----------------------------------------- Mean x, y : 0.0439, -0.0063 Standard deviation x, y: 7.9871, 4.7784 Rule 4: ----------------------------------------- Mean x, y : 3.1341, 5.4210 Standard deviation x, y: 1.5874, 3.9304
D
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);
}
- Output:
Rule 1: Mean x, y: 0.0004, 0.0702 Std dev x, y: 0.7153, 0.6462 Rule 2: Mean x, y: 0.0008, -0.0103 Std dev x, y: 1.0371, 0.8999 Rule 3: Mean x, y: 0.0438, -0.0063 Std dev x, y: 7.9871, 4.7784 Rule 4: Mean x, y: 3.1341, 5.4210 Std dev x, y: 1.5874, 3.9304
EasyLang
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 ]
#
proc funnel rule . dxs[] rxs[] .
rxs[] = [ ]
for dx in dxs[]
rxs[] &= x + dx
if rule = 1
x = 0
elif rule = 2
x = -dx
elif rule = 3
x = -(x + dx)
else
x = x + dx
.
.
.
proc mean . xs[] r .
r = 0
for x in xs[]
r += x
.
r /= len xs[]
.
proc stddev . xs[] r .
mean xs[] m
for x in xs[]
s += (x - m) * (x - m)
.
r = sqrt (s / len xs[])
.
proc experiment rule . .
funnel rule dxs[] rxs[]
funnel rule dys[] rys[]
print "Rule " & rule
mean rxs[] mx
mean rys[] my
print "Mean x, y : " & mx & " " & my
stddev rxs[] dx
stddev rys[] dy
print "Std dev x, y : " & dx & " " & dy
print ""
.
numfmt 4 0
experiment 1
experiment 2
experiment 3
experiment 4
Elixir
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)
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
Factor
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
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
FreeBASIC
Dim Shared As Double DXs(100) => {_
-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}
Dim Shared As Double DYs(100) => { _
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}
Function SumArray(arr() As Double) As Double
Dim As Double sum = 0.0
For i As Integer = Lbound(arr) To Ubound(arr)
sum += arr(i)
Next i
Return sum
End Function
Sub Funnel(DXs() As Double, rule As Integer, rxs() As Double)
Dim As Double x = 0.0
Dim As Integer i
For i = 1 To Ubound(dxs)
Dim As Double dx = DXs(i)
rxs(i) = x + dx
Select Case rule
Case 2: x = -dx
Case 3: x = -(x+dx)
Case 4: x = x+dx
End Select
Next i
End Sub
Function Mean(xs() As Double) As Double
Return SumArray(xs())/Ubound(xs)
End Function
Function StdDev(xs() As Double) As Double
Dim As Double m = Mean(xs())
Dim As Double sum = 0.0
For i As Integer = Lbound(xs) To Ubound(xs)
sum += (xs(i) - m) ^ 2
Next i
Return Sqr(sum / Ubound(xs))
End Function
Sub experiment(n As Integer, DXs() As Double, DYs() As Double)
Dim As Double rxs(Ubound(dxs)), rys(Ubound(dys))
Funnel(DXs(), n, rxs())
Funnel(DYs(), n, rys())
Print Using "Mean x, y : ###.####, ###.####"; mean(rxs()); mean(rys())
Print Using "Std dev x, y : ###.####, ###.####"; stddev(rxs()); stddev(rys())
End Sub
For i As Integer = 1 To 4
experiment(i, DXs(), DYs())
Next i
Sleep
- Output:
Mean x, y : 0.0057, 0.0689 Std dev x, y : 0.7133, 0.6462 Mean x, y : -0.0000, 0.0000 Std dev x, y : 1.0330, 0.9068 Mean x, y : -0.0381, 0.0752 Std dev x, y : 7.5940, 4.7279 Mean x, y : 3.6729, 5.3539 Std dev x, y : 1.6174, 3.9340
Go
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
})
}
- Output:
Rule 1 : x y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : x y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : x y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : x y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
Haskell
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)
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
J
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
Displayed result:
Rule 1 (x,y): Mean: 0.0004 0.07023 Std dev: 0.718875 0.649462 Rule 2 (x,y): Mean: 0.04386 _0.0063 Std dev: 8.02735 4.80249 Rule 3 (x,y): Mean: 0.00087 _0.01032 Std dev: 1.04236 0.904482 Rule 4 (x,y): Mean: _7e_5 0.15078 Std dev: 0.990174 0.918942
Author's note: these numbers are different from those of other implementations. I claim that this represents errors in the other implementations and invite proof that I am wrong.
Java
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);
}
}
Rule 1: Mean x, y: 0,0004, 0,0702 Std dev x, y: 0,7153, 0,6462 Rule 2: Mean x, y: 0,0009, -0,0103 Std dev x, y: 1,0371, 0,8999 Rule 3: Mean x, y: 0,0439, -0,0063 Std dev x, y: 7,9871, 4,7784 Rule 4: Mean x, y: 3,1341, 5,4210 Std dev x, y: 1,5874, 3,9304
jq
Adapted from Wren
Works with gojq, the Go implementation of jq, and with fq
Preliminaries
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);The Task
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- Output:
Rule 1 : x y Mean : 0.0004 0.0702 Std Dev : 0.7153 0.6462 Rule 2 : x y Mean : 0.0009 -0.0103 Std Dev : 1.0371 0.8999 Rule 3 : x y Mean : 0.0439 -0.0063 Std Dev : 7.9871 4.7784 Rule 4 : x y Mean : 3.1341 5.421 Std Dev : 1.5874 3.9304
Julia
# 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)
- Output:
Using Racket data. Rule 1 results: mean x: 0.0004 std x: 0.7153 mean y: 0.0702 std y: 0.6462 Rule 2 results: mean x: 0.0009 std x: 1.0371 mean y: -0.0103 std y: 0.8999 Rule 3 results: mean x: 0.0439 std x: 7.9871 mean y: -0.0063 std y: 4.7784 Rule 4 results: mean x: 3.1341 std x: 1.5874 mean y: 5.421 std y: 3.9304 Using new data. Rule 1 results: mean x: -0.0814 std x: 0.7761 mean y: -0.0187 std y: 0.799 Rule 2 results: mean x: 0.0009 std x: 0.9237 mean y: 0.0028 std y: 0.9626 Rule 3 results: mean x: 0.0123 std x: 4.7695 mean y: 0.0658 std y: 3.7198 Rule 4 results: mean x: -6.7132 std x: 4.5367 mean y: 1.632 std y: 2.0975
Kotlin
// 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 }
}
- Output:
Rule 1 : x y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : x y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : x y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : x y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
Mathematica /Wolfram Language
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]
- Output:
Rule 1
mean: {0.0004,0.07023}
std dev: {0.715271,0.646206}
Rule 2
mean: {0.00087,-0.01032}
std dev: {1.03714,0.899948}
Rule 3
mean: {0.04386,-0.0063}
std dev: {7.98712,4.77842}
Rule 4
mean: {3.13412,5.42102}
std dev: {1.58739,3.93036}
Stretch 1
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]
- Output:
Rule 1
mean: {0.0236483,-0.0480581}
std dev: {0.75398,0.678437}
Rule 2
mean: {-0.00586115,0.00205628}
std dev: {1.07625,0.922341}
Rule 3
mean: {0.0180857,-0.0707311}
std dev: {2.53086,4.29764}
Rule 4
mean: {1.78937,-0.132491}
std dev: {2.36082,3.15051}
Stretch 2
ListPlot[MarblePositions[#][Transpose[{dxs,dys}]]&/@Range[4],PlotLegends->PointLegend[{1,2,3,4}],AspectRatio->Automatic,ImageSize->600]
- Output:
~images disabled~
Nim
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)
- Output:
Rule 1 Mean x, y : 0.0004 0.0702 Std dev x, y : 0.7153 0.6462 Rule 2 Mean x, y : 0.0009 -0.0103 Std dev x, y : 1.0371 0.8999 Rule 3 Mean x, y : 0.0439 -0.0063 Std dev x, y : 7.9871 4.7784 Rule 4 Mean x, y : 3.1341 5.4210 Std dev x, y : 1.5874 3.9304
PARI/GP
- This is a work-in-progress.
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()
)
}PascalABC.NET
const
Dxs: array of real =
(-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: array of real =
(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);
function stddev(a: array of real) := a.Sum(x -> Sqr(x - a.average) / a.length).Sqrt;
function funnel(a: array of real; rule: (real, real) -> real): array of real;
begin
var x := 0.0;
setlength(result, a.length);
foreach var val in a index i do
begin
result[i] := x + val;
x := rule(x, val)
end;
end;
procedure experiment(lab: string; r: (real, real) -> real);
begin
var rxs := funnel(Dxs, r);
var rys := funnel(Dys, r);
lab.println;
writeln('Mean x, y: ', rxs.average:6:4, rys.average:8:4);
writeln('Std dev x, y: ', stddev(rxs):6:4, stddev(rys):8:4);
println;
end;
begin
experiment('Rule 1', (z, dz) -> 0.0);
experiment('Rule 2', (z, dz) -> -dz);
experiment('Rule 3', (z, dz) -> -(z + dz));
experiment('Rule 4', (z, dz) -> z + dz);
end.
- Output:
Rule 1 Mean x, y: 0.0004 0.0702 Std dev x, y: 0.7153 0.6462 Rule 2 Mean x, y: 0.0009 -0.0103 Std dev x, y: 1.0371 0.8999 Rule 3 Mean x, y: 0.0439 -0.0063 Std dev x, y: 7.9871 4.7784 Rule 4 Mean x, y: 3.1341 5.4210 Std dev x, y: 1.5874 3.9304
Perl
@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);
}
- Output:
Rule 1 Mean x, y : 0.0004 0.0702 Std dev x, y : 0.7153 0.6462 Rule 2 Mean x, y : 0.0009 -0.0103 Std dev x, y : 1.0371 0.8999 Rule 3 Mean x, y : 0.0439 -0.0063 Std dev x, y : 7.9871 4.7784 Rule 4 Mean x, y : 3.1341 5.4210
Std dev x, y : 1.5874 3.9304
Phix
with javascript_semantics function funnel(sequence dxs, integer rule) atom x = 0.0 sequence rxs = {} for i=1 to length(dxs) do atom dx = dxs[i] rxs = append(rxs,x + dx) switch rule case 2: x = -dx case 3: x = -(x+dx) case 4: x = x+dx end switch end for return rxs end function function mean(sequence xs) return sum(xs)/length(xs) end function function stddev(sequence xs) atom m = mean(xs) return sqrt(sum(sq_power(sq_sub(xs,m),2))/length(xs)) end function procedure experiment(integer n, sequence dxs, dys) sequence rxs = funnel(dxs,n), rys = funnel(dys,n) printf(1,"Mean x, y : %7.4f, %7.4f\n",{mean(rxs), mean(rys)}) printf(1,"Std dev x, y : %7.4f, %7.4f\n",{stddev(rxs), stddev(rys)}) end procedure constant 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} constant 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} for i=1 to 4 do experiment(i, dxs, dys) end for
- Output:
Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
Python
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)
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
Alternative: [Generates pseudo-random data and gives some interpretation.] The funnel experiment is performed in one dimension. The other dimension would act similarly.
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)
- Output:
Deming simulation. 5 trials using rule D1:
Keep Funnel over target.
Mean: -0.161, Sdev: 0.942
Mean: -0.092, Sdev: 0.924
Mean: -0.199, Sdev: 1.079
Mean: -0.256, Sdev: 0.820
Mean: -0.211, Sdev: 0.971
Should have smallest deviations ~1.0, and be centered on 0.0
Deming simulation. 5 trials using rule D2:
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.
Mean: -0.067, Sdev: 4.930
Mean: 0.035, Sdev: 4.859
Mean: -0.080, Sdev: 2.575
Mean: 0.147, Sdev: 4.948
Mean: 0.050, Sdev: 4.149
Should be centred on 0.0 with larger deviations than D1
Deming simulation. 5 trials using rule D3:
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.
Mean: 0.006, Sdev: 1.425
Mean: -0.039, Sdev: 1.436
Mean: 0.030, Sdev: 1.305
Mean: 0.009, Sdev: 1.419
Mean: 0.001, Sdev: 1.479
Should be centred on 0.0 with larger deviations than D1
Deming simulation. 5 trials using rule D4:
(Dumb). The new target is where it last dropped.
Mean: 5.252, Sdev: 2.839
Mean: 1.403, Sdev: 3.073
Mean: -1.525, Sdev: 3.650
Mean: 3.844, Sdev: 2.715
Mean: -7.697, Sdev: 3.715
Center wanders all over the place, with deviations to match!
Racket
The stretch solutions can be obtained by uncommenting radii etc. (delete the 4 semi-colons) to generate fresh data, and scatter-plots can be obtained by deleting the #; .
#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)))
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y: 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y: 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y: 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y: 1.5874, 3.9304
Raku
(formerly Perl 6)
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);
}
- Output:
Rule 1: Mean x, y : 0.0004 0.0702 Std dev x, y : 0.7153 0.6462 Rule 2: Mean x, y : 0.0009 -0.0103 Std dev x, y : 1.0371 0.8999 Rule 3: Mean x, y : 0.0439 -0.0063 Std dev x, y : 7.9871 4.7784 Rule 4: Mean x, y : 3.1341 5.4210 Std dev x, y : 1.5874 3.9304
Ruby
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}
- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304
Rust
use statrs::statistics::Statistics;
fn funnel(pseudo_random: &Vec<f64>, rule: fn(f64, f64) -> f64) -> Vec<f64> {
let mut value = 0.0;
let mut result = vec![0.0; pseudo_random.len()];
for i in 0..pseudo_random.len() {
result[i] = value + pseudo_random[i];
value = rule(value, pseudo_random[i]);
}
return result;
}
fn experiment(label: &str, pseudo_random_xs: &Vec<f64>, pseudo_random_ys: &Vec<f64>, rule: fn(f64, f64) -> f64) {
let result_x = funnel(pseudo_random_xs, rule);
let result_y = funnel(pseudo_random_ys, rule);
println!("{}\n{}", label, "-----------------------------------------");
println!("Mean x, y: {:>8.4}, {:<8.4}", (&result_x).mean(), (&result_y).mean());
println!("Standard deviation x, y:{:>8.4}, {:<8.4}\n", result_x.std_dev(), result_y.std_dev());
}
fn main() {
let pseudo_random_xs = vec![ -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 pseudo_random_ys = vec![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:", &pseudo_random_xs, &pseudo_random_ys, |_z, _dz| {0.0});
experiment("Rule 2:", &pseudo_random_xs, &pseudo_random_ys, |_z, dz| {-dz});
experiment("Rule 3:", &pseudo_random_xs, &pseudo_random_ys, |z, dz| {-(z + dz)});
experiment("Rule 4:", &pseudo_random_xs, &pseudo_random_ys, |z, dz| {z + dz});
}
- Output:
Rule 1: ----------------------------------------- Mean x, y: 0.0004, 0.0702 Standard deviation x, y: 0.7189, 0.6495 Rule 2: ----------------------------------------- Mean x, y: 0.0009, -0.0103 Standard deviation x, y: 1.0424, 0.9045 Rule 3: ----------------------------------------- Mean x, y: 0.0439, -0.0063 Standard deviation x, y: 8.0274, 4.8025 Rule 4: ----------------------------------------- Mean x, y: 3.1341, 5.4210 Standard deviation x, y: 1.5954, 3.9502
Scala
object DemingsFunnel {
def main(args: Array[String]): Unit = {
val dxs = Array(
-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 = Array(
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)
}
def experiment(label: String, dxs: Array[Double], dys: Array[Double], rule: (Double, Double) => Double): Unit = {
val resx = funnel(dxs, rule)
val resy = funnel(dys, rule)
println(label)
printf("Mean x, y: %.4f, %.4f%n", mean(resx), mean(resy))
printf("Std dev x, y: %.4f, %.4f%n", stdDev(resx), stdDev(resy))
println()
}
def funnel(input: Array[Double], rule: (Double, Double) => Double): Array[Double] = {
var x = 0.0
val result = new Array[Double](input.length)
for (i <- input.indices) {
val rx = x + input(i)
x = rule(x, input(i))
result(i) = rx
}
result
}
def mean(xs: Array[Double]): Double = xs.sum / xs.length
def stdDev(xs: Array[Double]): Double = {
val m = mean(xs)
math.sqrt(xs.map(x => math.pow((x - m), 2)).sum / xs.length)
}
}
- Output:
Rule 1: Mean x, y: 0.0004, 0.0702 Std dev x, y: 0.7153, 0.6462 Rule 2: Mean x, y: 0.0009, -0.0103 Std dev x, y: 1.0371, 0.8999 Rule 3: Mean x, y: 0.0439, -0.0063 Std dev x, y: 7.9871, 4.7784 Rule 4: Mean x, y: 3.1341, 5.4210 Std dev x, y: 1.5874, 3.9304
Sidef
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}))
}
- Output:
Rule 1: Mean x, y : 0.0004 0.0702 Std dev x, y : 0.7153 0.6462 Rule 2: Mean x, y : 0.0009 -0.0103 Std dev x, y : 1.0371 0.8999 Rule 3: Mean x, y : 0.0439 -0.0063 Std dev x, y : 7.9871 4.7784 Rule 4: Mean x, y : 3.1341 5.4210 Std dev x, y : 1.5874 3.9304
Swift
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 })
- Output:
Rule 1 : x y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : x y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : x y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : x y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
Tcl
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+$dz}}}
The first stretch goal:
package require math::constants
package require simulation::random
math::constants::constants degtorad
set rng(radius) [simulation::random::prng_Normal 0.0 1.0]
set rng(angle) [simulation::random::prng_Uniform 0.0 360.0]
set dxs [set dys {}]
for {set i 0} {$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}}}
- Output:
USING STANDARD DATA Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304 USING RANDOM DATA Rule 1: Mean x, y : 0.0053, 0.0112 Std dev x, y : 0.4954, 0.5082 Rule 2: Mean x, y : -0.0012, -0.0002 Std dev x, y : 0.6914, 0.7331 Rule 3: Mean x, y : -0.0132, 0.0098 Std dev x, y : 9.3480, 5.0290 Rule 4: Mean x, y : -6.3314, -4.0168 Std dev x, y : 3.2387, 4.4825
V (Vlang)
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
})
}- Output:
Rule 1 : x y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : x y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : x y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : x y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
Wren
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")
Fmt.print("Mean : $7.4f, $7.4f", Nums.mean(rxs), Nums.mean(rys))
Fmt.print("Std Dev : $7.4f, $7.4f", Nums.popStdDev(rxs), Nums.popStdDev(rys))
Fmt.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 }
- Output:
Rule 1 : x y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : x y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : x y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : x y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
XPL0
Works on RPi. MAlloc works differently in DOS versions and in EXPL.
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)- Output:
Rule 1 : X Y Mean : 0.0004, 0.0702 Std Dev : 0.7153, 0.6462 Rule 2 : X Y Mean : 0.0009, -0.0103 Std Dev : 1.0371, 0.8999 Rule 3 : X Y Mean : 0.0439, -0.0063 Std Dev : 7.9871, 4.7784 Rule 4 : X Y Mean : 3.1341, 5.4210 Std Dev : 1.5874, 3.9304
zkl
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();
}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 });- Output:
Rule 1: Mean x, y : 0.0004, 0.0702 Std dev x, y : 0.7153, 0.6462 Rule 2: Mean x, y : 0.0009, -0.0103 Std dev x, y : 1.0371, 0.8999 Rule 3: Mean x, y : 0.0439, -0.0063 Std dev x, y : 7.9871, 4.7784 Rule 4: Mean x, y : 3.1341, 5.4210 Std dev x, y : 1.5874, 3.9304