M3201 - TP1

import numpy as np

x = var('D1')
y = var('D2')
z = var('D3')

d1 = 0.9 * x + 0.7 * y + 0.8 * z - x == 0
d2 = 0.05 * x - y == 0
d3 = 0.05 * x + 0.3 * y + 0.2 * z - z == 0
d4 = x + y + z == 1

solution = solve([d1,d2,d3,d4], x,y,z)

d = solution[0][0].right()
m = solution[0][1].right()
j = solution[0][2].right()

show('D =' + str(round(d,5)) + ', M =' + str(round(m,5)) + ', J =' + str(round(j,5)))

dico = {"Dormir": 1,"Manger": 2, "Jouer": 3}

def Markov1pas(etat_init):
    r = random()
    if etat_init == dico["Dormir"]:
        if r <= 0.05:
            return dico["Manger"]
        elif r > 0.05 and r <= 0.1:
            return dico["Jouer"]
        else:
            return dico["Dormir"]
    elif etat_init == dico["Manger"]:
        if r <= 0.3:
            return dico["Jouer"]
        else:
            return dico["Dormir"]
    elif etat_init == dico["Jouer"]:
        if r <= 0.8:
            return dico["Dormir"]
        else:
            return dico["Jouer"]
    else:
        return -1

def TempsEtats(etat_init, n):
    D = 0
    M = 0
    J = 0
    for i in range(n):
        if etat_init == dico["Dormir"]:
            D += 1
        elif etat_init == dico["Manger"]:
            M += 1
        elif etat_init == dico["Jouer"]:
            J += 1
        etat_init = Markov1pas(etat_init)
    print('Domir : ' + str(D) + ' minutes.')
    print('Manger : ' + str(M) + ' minutes.')
    print('Jouer : ' + str(J) + ' minutes.')
    print('\n')
    print('P(D)= ' + str(round(D/n, 5)))
    print('P(M)= ' + str(round(M/n, 5)))
    print('P(J)= ' + str(round(J/n, 5)))

TempsEtats(1,6000)