Step by Step solution about How to resolve the algorithm Deming's funnel step by step in the Haskell programming language

This Haskell code defines a function funnel that takes a binary operator and a list of values and applies the operator to each pair of consecutive values in the list, returning the list of the results. It also defines functions to calculate the mean and standard deviation of a list of values.

The experiment function is the main function of the program. It takes a label, two lists of values, and a binary operator, then calculates and prints the mean and standard deviation of the results of applying the operator to each pair of values in the lists.

The code is used to test four different rules:

• Rule 1: No operation
• Rule 2: Subtract the second value from the first
• Rule 3: Subtract the sum of the two values from the second value
• Rule 4: Add the two values

Here is a breakdown of the code:

• The funnel function takes a binary operator and a list of values as input, and returns the list of the results of applying the operator to each pair of consecutive values in the list. For example, if the operator is + and the list is [1, 2, 3, 4, 5], the result will be [3, 5, 7, 9]. The code uses the mapAccumL function from the Data.List module to do this. The mapAccumL function takes a binary operator, an initial value, and a list, and returns the list of the results of applying the operator to each element in the list, starting with the initial value. In this case, the initial value is 0 and the operator is the binary operator passed to the funnel function.

• The mean function takes a list of values as input, and returns the mean of the values. The code uses the sum function from the Data.List module to calculate the sum of the values, and the genericLength function from the Data.List module to calculate the length of the list. The mean is then calculated by dividing the sum of the values by the length of the list.

• The stddev function takes a list of values as input, and returns the standard deviation of the values. The code uses the sum function from the Data.List module to calculate the sum of the squared differences between each value and the mean. The standard deviation is then calculated by taking the square root of the sum of the squared differences divided by the length of the list.

• The experiment function takes a label, two lists of values, and a binary operator as input, and prints the mean and standard deviation of the results of applying the operator to each pair of values in the lists. The code first calls the funnel function to calculate the list of results, then calls the mean and stddev functions to calculate the mean and standard deviation of the results. The results are then printed to the console.

• The main function calls the experiment function four times, using different labels, lists of values, and binary operators each time. The results are printed to the console.

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)