How to resolve the algorithm Probabilistic choice step by step in the Fortran programming language

Published on 12 May 2024 09:40 PM
#Fortran

How to resolve the algorithm Probabilistic choice step by step in the Fortran programming language

Table of Contents

Problem Statement

Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values. The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Probabilistic choice step by step in the Fortran programming language

Source code in the fortran programming language

PROGRAM PROBS
 
  IMPLICIT NONE
   
  INTEGER, PARAMETER :: trials = 1000000
  INTEGER :: i, j, probcount(8) = 0
  REAL :: expected(8), mapping(8), rnum
  CHARACTER(6) :: items(8) = (/ "aleph ", "beth  ", "gimel ", "daleth", "he    ", "waw   ", "zayin ", "heth  " /)

  expected(1:7) = (/ (1.0/i, i=5,11) /)
  expected(8) = 1.0 - SUM(expected(1:7))
  mapping(1) = 1.0 / 5.0
  DO i = 2, 7
     mapping(i) = mapping(i-1) + 1.0/(i+4.0)
  END DO
  mapping(8) = 1.0

  DO i = 1, trials
     CALL RANDOM_NUMBER(rnum)
     DO j = 1, 8
        IF (rnum < mapping(j)) THEN
           probcount(j) = probcount(j) + 1
           EXIT
        END IF
     END DO
  END DO

  WRITE(*, "(A,I10)") "Trials:             ", trials
  WRITE(*, "(A,8A10)") "Items:             ", items
  WRITE(*, "(A,8F10.6)") "Target Probability:  ", expected
  WRITE(*, "(A,8F10.6)") "Attained Probability:", REAL(probcount) / REAL(trials)
  
ENDPROGRAM PROBS

You may also check:How to resolve the algorithm Scope modifiers step by step in the 68000 Assembly programming language
You may also check:How to resolve the algorithm Pick random element step by step in the jq programming language
You may also check:How to resolve the algorithm Grayscale image step by step in the FreeBASIC programming language
You may also check:How to resolve the algorithm Earliest difference between prime gaps step by step in the Pascal programming language
You may also check:How to resolve the algorithm Shoelace formula for polygonal area step by step in the Kotlin programming language