How to resolve the algorithm Modified random distribution step by step in the Haskell programming language

Published on 7 June 2024 03:52 AM

How to resolve the algorithm Modified random distribution step by step in the Haskell programming language

Table of Contents

Problem Statement

Given a random number generator, (rng), generating numbers in the range 0.0 .. 1.0 called rgen, for example; and a function modifier(x) taking an number in the same range and generating the probability that the input should be generated, in the same range 0..1; then implement the following algorithm for generating random numbers to the probability given by function modifier:

Show your output here, on this page.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Modified random distribution step by step in the Haskell programming language

The Haskell source code defines three functions: modify, vShape, and hist. Here's an explanation of each function:

  1. modify: This function takes two arguments:

    • f: A function that takes an element of type a and returns an element of type a.
    • lst: A list of elements of type a.

    The modify function applies the f function to each element of the list, and then removes elements from the list when the next element is smaller than the previous element after applying f.

  2. vShape: This function takes one argument:

    • x: A numerical value

    The vShape function calculates a V-shaped value based on the input x. It returns 2*(0.5-x) if x is less than 0.5, and 2*(x-0.5) otherwise.

  3. hist: This function takes two arguments:

    • b: A numerical value representing the bin size
    • lst: A list of numerical values

    The hist function calculates a histogram of distribution for the lst of values. It divides each value in the list by the bin size b, rounds the result to the nearest integer, and groups the rounded values together. The frequency of each rounded value is then calculated, and the result is converted into a list of tuples, where each tuple contains a bin value and the frequency of that bin.

Here's an example usage of the hist function:

import System.Random

main :: IO ()
main = do
 -- Generate a list of 100 random numbers between 0 and 1
 g <- getStdGen
 let lst = map (/10) $ randoms g :: [Double]

 -- Create a histogram with a bin size of 0.1
 let h = hist 0.1 lst

 -- Print the histogram
 showHist h

This example will generate a histogram of the random numbers in the list lst and print the result. Each bin in the histogram will represent a range of 0.1. For example, the output might look something like this:

0.00  ▇ 10%
0.10  ▇▇ 20%
0.20  ▇▇▇▇ 40%
0.30  ▇▇▇ 30%

Source code in the haskell programming language

import System.Random
import Data.List
import Text.Printf

modify :: Ord a => (a -> a) -> [a] -> [a]
modify f = foldMap test . pairs 
  where
    pairs lst = zip lst (tail lst)
    test (r1, r2) = if r2 < f r1 then [r1] else []

vShape x = if x < 0.5 then 2*(0.5-x) else 2*(x-0.5)

hist b lst = zip [0,b..] res
  where
    res = (`div` sum counts) . (*300) <$> counts
    counts = map length $ group $
             sort $ floor . (/b) <$> lst

showHist h = foldMap mkLine h
  where
    mkLine (b,n) = printf "%.2f\t%s %d%%\n" b (replicate n '▇') n


  

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