Task: Deming's funnel





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);
    }
}



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)