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Delete Projet Numérique/.virtual_documents directory
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import numpy as np
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import matplotlib.pyplot as plt
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import numpy.random as random
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import itertools
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class ModeleSchelling:
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def __init__(self, M, p, L):
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self.M = M
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self.p = p
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self.L = L
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self.Ntot = 0
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self.grille = self.initialisation_grille()
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def initialisation_grille(self):
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grille = np.zeros((self.M, self.M), dtype=int)
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occupes = np.random.choice(self.M * self.M, size=int((1 - self.p) * self.M * self.M), replace=False)
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self.Ntot = len(occupes)
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for occupe in occupes:
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i, j = divmod(occupe, self.M)
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grille[i, j] = random.choice([-1, 1])
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return grille
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def afficher_grille(self, title):
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color = plt.imshow(self.grille, cmap='coolwarm', interpolation='nearest')
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plt.colorbar(color)
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plt.title(title)
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plt.show()
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def satisfaisante(self, x, y, agent):
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groupe = self.grille[agent[0], agent[1]]
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count_similaires = 0
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count_differents = 0
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voisins = []
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for (i,j) in list(itertools.product([x-1, x, x+1], [y-1, y, y+1])):
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if 0 <= i < self.M and 0 <= j < self.M and (i, j) != (x, y):
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voisins.append((i, j))
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for voisin in voisins:
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i, j = voisin
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case = self.grille[i, j]
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if case == 0: pass
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else:
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if case == groupe:
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count_similaires += 1
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else:
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count_differents += 1
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if count_similaires+count_differents == 0:
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return False
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else:
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return float(count_similaires/(count_similaires+count_differents)) >= self.L
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def clusters(self):
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visited = np.zeros_like(self.grille, dtype=bool)
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clusters = []
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def dfs(i, j, groupe, cluster):
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stack = [(i, j)]
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while stack:
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i, j = stack.pop()
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if 0 <= i < self.M and 0 <= j < self.M and not visited[i, j] and self.grille[i, j] == groupe:
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visited[i, j] = True
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cluster.add((i, j))
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for (di, dj) in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
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stack.append((i + di, j + dj))
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added_clusters = set()
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for groupe in [-1, 1]:
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indices = np.argwhere((self.grille == groupe) & (~visited))
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for i, j in indices:
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current_cluster = set()
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dfs(i, j, groupe, current_cluster)
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if current_cluster and frozenset(current_cluster) not in added_clusters:
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clusters.append((groupe, len(current_cluster)))
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added_clusters.add(frozenset(current_cluster))
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return clusters
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def coef_segregation(self):
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S = 0
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clusters = self.clusters()
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for i in range(len(clusters)):
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S += int(clusters[i][1])**2
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return S * 2 / (self.Ntot**2)
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def simuler(self, T=400, move_satisfaits=True):
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for t in range(1, int((1-self.p)*self.M**2 * T)):
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agents = [(i, j) for i, row in enumerate(self.grille) for j, val in enumerate(row) if val != 0]
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agent = agents[random.randint(0, len(agents) - 1)]
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while not move_satisfaits and self.satisfaisante(agent[0], agent[1], agent):
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agents.remove(agent)
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if len(agents) == 0:
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break
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agent = agents[random.randint(0, len(agents) - 1)]
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cases_non_occupees = [(i, j) for i, row in enumerate(self.grille) for j, val in enumerate(row) if val == 0]
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nouvelle_case = cases_non_occupees[random.randint(0, len(cases_non_occupees) - 1)]
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while not self.satisfaisante(nouvelle_case[0], nouvelle_case[1], agent):
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cases_non_occupees.remove(nouvelle_case)
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if len(cases_non_occupees) == 0:
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break
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nouvelle_case = cases_non_occupees[random.randint(0, len(cases_non_occupees) - 1)]
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self.grille[nouvelle_case[0]][nouvelle_case[1]] = self.grille[agent[0]][agent[1]]
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self.grille[agent[0]][agent[1]] = 0
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cases_non_occupees.append(agent)
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self.afficher_grille(f'Configuration Finale de T={T} pour (M, p, L) = ({self.M},{self.p},{self.L})')
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M = 100
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p = 5/100
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L = 1/2
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modele = ModeleSchelling(M, p, L)
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modele.afficher_grille("Configuration Initiale")
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for T in [1, 10, 100, 400]:
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modele.simuler(T, True)
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M = 50
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T = 400
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p_list = [2/100, 6/100, 12/100, 18/100]
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L_list = [1/5, 2/7, 1/3, 5/7, 3/4]
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for p in p_list:
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for L in L_list:
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modele = ModeleSchelling(M, p, L)
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modele.afficher_grille(f"Configuration Initiale pour p={p} et L={L}")
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modele.simuler(T, False)
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M = 40
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T = 400
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p = 5/100
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L = 2/7
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modele = ModeleSchelling(M, p, L)
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modele.afficher_grille("Configuration Initiale")
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modele.simuler(T)
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print(modele.clusters())
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print(len(modele.clusters()))
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print(modele.coef_segregation())
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