simusRandomQuestions/scriptSimus.py at master · JulienLefevreMars/simusRandomQuestions · GitHub

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import numpy as np
import matplotlib.pyplot as plt

#########################################
#                                       #
# Simulations and Distances computation #
#                                       #
#########################################

def mainSimulation(params):
    (nbQuestionsPerStudent,nbStudents,nbStudentsPerGroup)=params
    nbQuestions = np.arange(nbQuestionsPerStudent+1,nbStudents*nbQuestionsPerStudent,5)

    meanPWDistances=np.zeros((len(nbQuestions),))
    minmaxPWDistances=np.zeros((len(nbQuestions),2))
    meanDistances=np.zeros((len(nbQuestions),))
    minmaxDistances=np.zeros((len(nbQuestions),2))
    cpt=0
    for n in nbQuestions:

        # Generate nbQuestions random partitions of the set {0,n}
        randperm = np.zeros((nbQuestionsPerStudent,nbStudentsPerGroup))
        for i in range(nbStudentsPerGroup):
            randperm[:,i]=np.random.permutation(n)[0:nbQuestionsPerStudent]

        # Compute all pairwise distances between partitions (edit distance)
        distance=[]
        unionOfIntersect=[]
        for i in range(nbStudentsPerGroup):
            for j in range(nbStudentsPerGroup):
                if i<j:
                    unionOfIntersect.append(np.intersect1d(randperm[:,i],randperm[:,j]))
                    dist=len(np.intersect1d(randperm[:,i],randperm[:,j]))
                    distance.append(dist)
        meanPWDistances[cpt]=np.mean(np.array(distance))
        minmaxPWDistances[cpt,0]=np.min(np.array(distance))
        minmaxPWDistances[cpt,1]=np.max(np.array(distance))

        # Union of all questions => diff between individual questions and union
        union=np.unique(randperm.flatten())
        distance=[]
        unionOfIntersect=np.unique(np.concatenate(unionOfIntersect))
        for i in range(nbStudentsPerGroup):
            dist=len(np.setdiff1d(randperm[:,i],unionOfIntersect))
            distance.append(dist)
        meanDistances[cpt]=np.mean(np.array(distance))
        minmaxDistances[cpt,0]=np.min(np.array(distance))
        minmaxDistances[cpt,1]=np.max(np.array(distance))
        cpt=cpt+1
    return (meanPWDistances,minmaxPWDistances,meanDistances,minmaxDistances,nbQuestions)

#################
#               #
# Visualization #
#               #
#################

def vizu(nbQuestions,meanPWDistances,minmaxPWDistances,meanDistances,minmaxDistances,params):
    (nbQuestionsPerStudent,nbStudents,nbStudentsPerGroup)=params

    plt.figure(figsize=(12,8))
    plt.semilogx(nbQuestions,meanPWDistances,'k-')
    plt.fill_between(nbQuestions,minmaxPWDistances[:,0],minmaxPWDistances[:,1])
    plt.xlabel('Number of all the questions required for the exam')
    plt.ylabel('Questions')
    plt.legend(['Average','Min-Max for '+str(nbStudentsPerGroup)+' students per group'])
    plt.title('Shared questions between two exam subjects with ' + str(nbQuestionsPerStudent) + ' questions')
    plt.savefig("Figure1.png")
    plt.show()

    plt.figure(figsize=(12,8))
    plt.semilogx(nbQuestions,nbQuestionsPerStudent-meanDistances,'k-')
    plt.fill_between(nbQuestions,nbQuestionsPerStudent-minmaxDistances[:,0],nbQuestionsPerStudent-minmaxDistances[:,1])
    plt.xlabel('Number of all the questions required for the exam')
    plt.ylabel('Questions' )
    plt.legend(['Average','Min-Max for '+str(nbStudentsPerGroup)+' students per group'])
    plt.title('Questions among ' + str(nbQuestionsPerStudent) + ' shared in a group of '+str(nbStudentsPerGroup)+' students')
    plt.savefig("Figure2.png")
    plt.show()

    plt.figure(figsize=(12,8))
    plt.semilogx(nbQuestions,meanPWDistances,'r-')
    plt.semilogx(nbQuestions,nbQuestionsPerStudent-meanDistances,'b-')
    plt.legend(['Shared questions between two exam subjects','Questions shared in a group of '+str(nbStudentsPerGroup)+' students'])
    plt.savefig("Figure3.png")
    plt.show()

########
#      #
# Main #
#      #
########

if __name__ == '__main__':
    print('Number of students: \n')
    nbStudents=input()
    print('\n Number of questions: \n')
    nbQuestionsPerStudent=input()
    print('\n Number of students per group')
    nbStudentsPerGroup=input()
    params=(int(nbQuestionsPerStudent),int(nbStudents),int(nbStudentsPerGroup))

    (meanPWDistances,minmaxPWDistances,meanDistances,minmaxDistances,nbQuestions)=mainSimulation(params)
    vizu(nbQuestions,meanPWDistances,minmaxPWDistances,meanDistances,minmaxDistances,params)