291 lines
10 KiB
Python
Executable file
291 lines
10 KiB
Python
Executable file
#!/usr/bin/python3
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from random import random
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from math import floor, sqrt,factorial
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from statistics import mean, variance
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from matplotlib import pyplot as plt
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from pylab import *
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import numpy as np
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import matplotlib.pyplot as pt
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def simulate_NFBP(N):
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"""
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Tries to simulate T_i, V_i and H_n for N items of random size.
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"""
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i = 0 # Nombre de boites
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R = [0] # Remplissage de la i-eme boite
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T = [0] # Nombre de paquets de la i-eme boite
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V = [0] # Taille du premier paquet de la i-eme boite
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H = [] # Rang de la boite contenant le n-ieme paquet
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for n in range(N):
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size = random()
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if R[i] + size >= 1:
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# Il y n'y a plus de la place dans la boite pour le paquet.
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# On passe à la boite suivante (qu'on initialise)
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i += 1
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R.append(0)
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T.append(0)
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V.append(0)
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R[i] += size
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T[i] += 1
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if V[i] == 0:
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# C'est le premier paquet de la boite
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V[i] = size
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H.append(i)
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return {
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"i": i,
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"R": R,
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"T": T,
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"V": V,
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"H": H
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}
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# unused
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def stats_NFBP(R, N):
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"""
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Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
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"""
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print("Running {} NFBP simulations with {} items".format(R, N))
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I = []
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H = [[] for _ in range(N)] # List of empty lists
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for i in range(R):
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sim = simulate_NFBP(N)
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I.append(sim["i"])
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for n in range(N):
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H[n].append(sim["H"][n])
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print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
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for n in range(N):
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print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
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def stats_NFBP_iter(R, N):
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"""
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Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
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Calculates stats during runtime instead of after to avoid excessive memory usage.
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"""
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P=R*N # Total number of items
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print("## Running {} NFBP simulations with {} items".format(R, N))
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# number of bins
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ISum = 0
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IVarianceSum = 0
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# index of the bin containing the n-th item
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HSum = [0 for _ in range(N)]
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HSumVariance = [0 for _ in range(N)]
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# number of items in the i-th bin
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Sum_T=[0 for _ in range(N)]
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# size of the first item in the i-th bin
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Sum_V=[0 for _ in range(N)]
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for i in range(R):
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sim = simulate_NFBP(N)
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ISum += sim["i"]
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IVarianceSum += sim["i"]**2
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for n in range(N):
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HSum[n] += sim["H"][n]
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HSumVariance[n] += sim["H"][n]**2
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T=sim['T']
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V=sim['V']
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# ensure that T, V have the same length as Sum_T, Sum_V
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for i in range(N - sim['i']):
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T.append(0)
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V.append(0)
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Sum_T=[x+y for x,y in zip(Sum_T,T)]
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Sum_V=[x+y for x,y in zip(Sum_V,V)]
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Sum_T=[x/R for x in Sum_T]
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Sum_V=[round(x/R,2) for x in Sum_V]
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#print(Sum_V)
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I = ISum/R
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IVariance = sqrt(IVarianceSum/(R-1) - I**2)
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print("Mean number of bins : {} (variance {})".format(I, IVariance),'\n')
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# TODO clarify line below
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print(" {} * {} iterations of T".format(R,N),'\n')
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for n in range(min(N, 10)):
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Hn = HSum[n]/R # moyenne
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HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
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print("Index of bin containing the {}th item (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
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HSum=[x/R for x in HSum]
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# print(HSum)
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#Plotting
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fig = plt.figure()
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#T plot
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x = np.arange(N)
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# print(x)
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ax = fig.add_subplot(221)
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ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
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ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
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ax.set_ylabel('Items')
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ax.set_xlabel('Bins (1-{})'.format(N))
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ax.set_title('T histogram for {} items (Number of items in each bin)'.format(P))
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ax.legend(loc='upper left',title='Legend')
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#V plot
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bx = fig.add_subplot(222)
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bx.bar(x,Sum_V, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='orange')
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bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 1), yticks=np.linspace(0, 1, 10))
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bx.set_ylabel('First item size')
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bx.set_xlabel('Bins (1-{})'.format(N))
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bx.set_title('V histogram for {} items (first item size of each bin)'.format(P))
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bx.legend(loc='upper left',title='Legend')
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#H plot
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#We will simulate this part for a asymptotic study
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cx = fig.add_subplot(223)
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cx.bar(x,HSum, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='green')
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cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 10), yticks=np.linspace(0, N, 5))
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cx.set_ylabel('Bin ranking of n-item')
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cx.set_xlabel('n-item (1-{})'.format(N))
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cx.set_title('H histogram for {} items'.format(P))
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xb=linspace(0,N,10)
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yb=Hn*xb/10
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wb=HVariance*xb/10
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cx.plot(xb,yb,label='Theoretical E(Hn)',color='brown')
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cx.plot(xb,wb,label='Theoretical V(Hn)',color='purple')
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cx.legend(loc='upper left',title='Legend')
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plt.show()
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def simulate_NFDBP(N):
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"""
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Tries to simulate T_i, V_i and H_n for N items of random size.
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Next Fit Dual Bin Packing : bins should overflow
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"""
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i = 0 # Nombre de boites
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R = [0] # Remplissage de la i-eme boite
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T = [0] # Nombre de paquets de la i-eme boite
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V = [0] # Taille du premier paquet de la i-eme boite
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H = [] # Rang de la boite contenant le n-ieme paquet
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for n in range(N):
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size = random()
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R[i] += size
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T[i] += 1
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if R[i] + size >= 1:
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# Il y n'y a plus de la place dans la boite pour le paquet.
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# On passe à la boite suivante (qu'on initialise)
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i += 1
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R.append(0)
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T.append(0)
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V.append(0)
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if V[i] == 0:
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# C'est le premier paquet de la boite
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V[i] = size
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H.append(i)
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return {
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"i": i,
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"R": R,
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"T": T,
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"V": V,
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"H": H
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}
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def stats_NFDBP(R, N,t_i):
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"""
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Runs R runs of NFDBP (for N items) and studies distribution, variance, mean...
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"""
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print("## Running {} NFDBP simulations with {} items".format(R, N))
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P=N*R # Total number of items
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I = []
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H = [[] for _ in range(N)] # List of empty lists
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T=[]
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Tk=[[] for _ in range(N)]
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Ti=[]
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T_maths=[]
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#First iteration to use zip after
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sim=simulate_NFDBP(N)
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Sum_T=[0 for _ in range(N)]
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for i in range(R):
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sim = simulate_NFDBP(N)
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I.append(sim["i"])
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for k in range(N):
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T.append(0)
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T=sim["T"]
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for n in range(N):
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H[n].append(sim["H"][n])
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Tk[n].append(sim["T"][n])
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Ti.append(sim["T"])
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Sum_T=[x+y for x,y in zip(Sum_T,T)]
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Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k]
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Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items
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print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
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for n in range(N):
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print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
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print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
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#Loi math
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for u in range(N):
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u=u+2
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T_maths.append(1/(factorial(u-1))-1/factorial(u))
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E=0
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sigma2=0
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# print(T_maths)
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for p in range(len(T_maths)):
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E=E+(p+1)*T_maths[p]
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sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1)
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print("Mathematical values : Empiric mean T_{} : {} Variance {})".format(t_i, E, sqrt(sigma2)))
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T_maths=[x*100 for x in T_maths]
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#Plotting
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fig = plt.figure()
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#T plot
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x = np.arange(N)
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print(x)
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print(Sum_T)
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ax = fig.add_subplot(221)
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ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
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ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,20), yticks=np.linspace(0, 20, 2))
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ax.set_ylabel('Items(n) in %')
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ax.set_xlabel('Bins (1-{})'.format(N))
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ax.set_title('Items percentage for each bin and {} items (Number of items in each bin)'.format(P))
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ax.legend(loc='upper left',title='Legend')
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#Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
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print(len(Tk[t_i]))
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bx = fig.add_subplot(222)
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bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
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bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,len(Tk[t_i])), yticks=np.linspace(0, 1, 1))
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bx.set_ylabel('P(T{}=i)'.format(t_i))
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bx.set_xlabel('Bins i=(1-{}) in %'.format(N))
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bx.set_title('T{} histogram for {} items (Number of items in each bin)'.format(t_i,P))
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bx.legend(loc='upper left',title='Legend')
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#Loi mathematique
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print(T_maths)
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cx = fig.add_subplot(224)
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cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red')
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cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,100), yticks=np.linspace(0, 100, 10))
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cx.set_ylabel('P(T{}=i)'.format(t_i))
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cx.set_xlabel('Bins i=(1-{})'.format(N))
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cx.set_title('Theoretical T{} values in %'.format(t_i))
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cx.legend(loc='upper left',title='Legend')
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plt.show()
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# unused
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def basic_demo():
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N = 10 ** 1
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sim = simulate_NFBP(N)
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print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
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for j in range(sim["i"] + 1):
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remplissage = floor(sim["R"][j] * 100)
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print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j],
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sim["V"][j]))
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print()
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stats_NFBP(10 ** 3, 10)
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N = 10 ** 1
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sim = simulate_NFDBP(N)
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print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
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for j in range(sim["i"] + 1):
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remplissage = floor(sim["R"][j] * 100)
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print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage,
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sim["T"][j],
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sim["V"][j]))
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stats_NFBP_iter(10**3, 10)
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print('\n\n')
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stats_NFDBP(10 ** 3, 10,1)
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