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Paul ALNET 2023-06-04 08:27:24 +02:00
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commit 316c910c3a
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317
Probas.py
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@ -1,12 +1,13 @@
#!/usr/bin/python3 #!/usr/bin/python3
from random import random from random import random
from math import floor, sqrt,factorial from math import floor, sqrt, factorial
from statistics import mean, variance from statistics import mean, variance
from matplotlib import pyplot as plt from matplotlib import pyplot as plt
from pylab import * from pylab import *
import numpy as np import numpy as np
import matplotlib.pyplot as pt import matplotlib.pyplot as pt
def simulate_NFBP(N): def simulate_NFBP(N):
""" """
Tries to simulate T_i, V_i and H_n for N items of random size. Tries to simulate T_i, V_i and H_n for N items of random size.
@ -32,13 +33,7 @@ def simulate_NFBP(N):
V[i] = size V[i] = size
H.append(i) H.append(i)
return { return {"i": i, "R": R, "T": T, "V": V, "H": H}
"i": i,
"R": R,
"T": T,
"V": V,
"H": H
}
# unused # unused
@ -61,12 +56,13 @@ def stats_NFBP(R, N):
for n in range(N): for n in range(N):
print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n]))) print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
def stats_NFBP_iter(R, N): def stats_NFBP_iter(R, N):
""" """
Runs R runs of NFBP (for N items) and studies distribution, variance, mean... Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
Calculates stats during runtime instead of after to avoid excessive memory usage. Calculates stats during runtime instead of after to avoid excessive memory usage.
""" """
P=R*N # Total number of items P = R * N # Total number of items
print("## Running {} NFBP simulations with {} items".format(R, N)) print("## Running {} NFBP simulations with {} items".format(R, N))
# number of bins # number of bins
ISum = 0 ISum = 0
@ -75,77 +71,112 @@ def stats_NFBP_iter(R, N):
HSum = [0 for _ in range(N)] HSum = [0 for _ in range(N)]
HSumVariance = [0 for _ in range(N)] HSumVariance = [0 for _ in range(N)]
# number of items in the i-th bin # number of items in the i-th bin
Sum_T=[0 for _ in range(N)] Sum_T = [0 for _ in range(N)]
# size of the first item in the i-th bin # size of the first item in the i-th bin
Sum_V=[0 for _ in range(N)] Sum_V = [0 for _ in range(N)]
for i in range(R): for i in range(R):
sim = simulate_NFBP(N) sim = simulate_NFBP(N)
ISum += sim["i"] ISum += sim["i"]
IVarianceSum += sim["i"]**2 IVarianceSum += sim["i"] ** 2
for n in range(N): for n in range(N):
HSum[n] += sim["H"][n] HSum[n] += sim["H"][n]
HSumVariance[n] += sim["H"][n]**2 HSumVariance[n] += sim["H"][n] ** 2
T=sim['T'] T = sim["T"]
V=sim['V'] V = sim["V"]
# ensure that T, V have the same length as Sum_T, Sum_V # ensure that T, V have the same length as Sum_T, Sum_V
for i in range(N - sim['i']): for i in range(N - sim["i"]):
T.append(0) T.append(0)
V.append(0) V.append(0)
Sum_T=[x+y for x,y in zip(Sum_T,T)] Sum_T = [x + y for x, y in zip(Sum_T, T)]
Sum_V=[x+y for x,y in zip(Sum_V,V)] Sum_V = [x + y for x, y in zip(Sum_V, V)]
Sum_T=[x/R for x in Sum_T] Sum_T = [x / R for x in Sum_T]
Sum_V=[round(x/R,2) for x in Sum_V] Sum_V = [round(x / R, 2) for x in Sum_V]
#print(Sum_V) # print(Sum_V)
I = ISum/R I = ISum / R
IVariance = sqrt(IVarianceSum/(R-1) - I**2) IVariance = sqrt(IVarianceSum / (R - 1) - I**2)
print("Mean number of bins : {} (variance {})".format(I, IVariance),'\n') print("Mean number of bins : {} (variance {})".format(I, IVariance), "\n")
# TODO clarify line below # TODO clarify line below
print(" {} * {} iterations of T".format(R,N),'\n') print(" {} * {} iterations of T".format(R, N), "\n")
for n in range(min(N, 10)): for n in range(min(N, 10)):
Hn = HSum[n]/R # moyenne Hn = HSum[n] / R # moyenne
HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance HVariance = sqrt(HSumVariance[n] / (R - 1) - Hn**2) # Variance
print("Index of bin containing the {}th item (H_{}) : {} (variance {})".format(n, n, Hn, HVariance)) print(
HSum=[x/R for x in HSum] "Index of bin containing the {}th item (H_{}) : {} (variance {})".format(
n, n, Hn, HVariance
)
)
HSum = [x / R for x in HSum]
# print(HSum) # print(HSum)
#Plotting # Plotting
fig = plt.figure() fig = plt.figure()
#T plot # T plot
x = np.arange(N) x = np.arange(N)
# print(x) # print(x)
ax = fig.add_subplot(221) ax = fig.add_subplot(221)
ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red') ax.bar(
ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5)) x,
ax.set_ylabel('Items') Sum_T,
ax.set_xlabel('Bins (1-{})'.format(N)) width=1,
ax.set_title('T histogram for {} items (Number of items in each bin)'.format(P)) label="Empirical values",
ax.legend(loc='upper left',title='Legend') edgecolor="blue",
#V plot linewidth=0.7,
color="red",
)
ax.set(
xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 3), yticks=np.linspace(0, 3, 5)
)
ax.set_ylabel("Items")
ax.set_xlabel("Bins (1-{})".format(N))
ax.set_title("T histogram for {} items (Number of items in each bin)".format(P))
ax.legend(loc="upper left", title="Legend")
# V plot
bx = fig.add_subplot(222) bx = fig.add_subplot(222)
bx.bar(x,Sum_V, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='orange') bx.bar(
bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 1), yticks=np.linspace(0, 1, 10)) x,
bx.set_ylabel('First item size') Sum_V,
bx.set_xlabel('Bins (1-{})'.format(N)) width=1,
bx.set_title('V histogram for {} items (first item size of each bin)'.format(P)) label="Empirical values",
bx.legend(loc='upper left',title='Legend') edgecolor="blue",
#H plot linewidth=0.7,
#We will simulate this part for a asymptotic study color="orange",
)
bx.set(
xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 1), yticks=np.linspace(0, 1, 10)
)
bx.set_ylabel("First item size")
bx.set_xlabel("Bins (1-{})".format(N))
bx.set_title("V histogram for {} items (first item size of each bin)".format(P))
bx.legend(loc="upper left", title="Legend")
# H plot
# We will simulate this part for a asymptotic study
cx = fig.add_subplot(223) cx = fig.add_subplot(223)
cx.bar(x,HSum, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='green') cx.bar(
cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0, 10), yticks=np.linspace(0, N, 5)) x,
cx.set_ylabel('Bin ranking of n-item') HSum,
cx.set_xlabel('n-item (1-{})'.format(N)) width=1,
cx.set_title('H histogram for {} items'.format(P)) label="Empirical values",
xb=linspace(0,N,10) edgecolor="blue",
yb=Hn*xb/10 linewidth=0.7,
wb=HVariance*xb/10 color="green",
cx.plot(xb,yb,label='Theoretical E(Hn)',color='brown') )
cx.plot(xb,wb,label='Theoretical V(Hn)',color='purple') cx.set(
cx.legend(loc='upper left',title='Legend') xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 10), yticks=np.linspace(0, N, 5)
)
cx.set_ylabel("Bin ranking of n-item")
cx.set_xlabel("n-item (1-{})".format(N))
cx.set_title("H histogram for {} items".format(P))
xb = linspace(0, N, 10)
yb = Hn * xb / 10
wb = HVariance * xb / 10
cx.plot(xb, yb, label="Theoretical E(Hn)", color="brown")
cx.plot(xb, wb, label="Theoretical V(Hn)", color="purple")
cx.legend(loc="upper left", title="Legend")
plt.show() plt.show()
def simulate_NFDBP(N): def simulate_NFDBP(N):
""" """
Tries to simulate T_i, V_i and H_n for N items of random size. Tries to simulate T_i, V_i and H_n for N items of random size.
@ -172,119 +203,169 @@ def simulate_NFDBP(N):
R[i] += size R[i] += size
T[i] += 1 T[i] += 1
return { return {"i": i, "R": R, "T": T, "V": V, "H": H}
"i": i,
"R": R,
"T": T,
"V": V,
"H": H
}
def stats_NFDBP(R, N,t_i): def stats_NFDBP(R, N, t_i):
""" """
Runs R runs of NFDBP (for N items) and studies distribution, variance, mean... Runs R runs of NFDBP (for N items) and studies distribution, variance, mean...
""" """
print("## Running {} NFDBP simulations with {} items".format(R, N)) print("## Running {} NFDBP simulations with {} items".format(R, N))
P=N*R # Total number of items # TODO comment this function
P = N * R # Total number of items
I = [] I = []
H = [[] for _ in range(N)] # List of empty lists H = [[] for _ in range(N)] # List of empty lists
T=[] T = []
Tk=[[] for _ in range(N)] Tk = [[] for _ in range(N)]
Ti=[] Ti = []
T_maths=[] T_maths = []
#First iteration to use zip after # First iteration to use zip after
sim=simulate_NFDBP(N) sim = simulate_NFDBP(N)
Sum_T=[0 for _ in range(N)] Sum_T = [0 for _ in range(N)]
for i in range(R): for i in range(R):
sim = simulate_NFDBP(N) sim = simulate_NFDBP(N)
I.append(sim["i"]) I.append(sim["i"])
for k in range(N): for k in range(N):
T.append(0) T.append(0)
T=sim["T"] T = sim["T"]
for n in range(N): for n in range(N):
H[n].append(sim["H"][n]) H[n].append(sim["H"][n])
Tk[n].append(sim["T"][n]) Tk[n].append(sim["T"][n])
Ti.append(sim["T"]) Ti.append(sim["T"])
Sum_T=[x+y for x,y in zip(Sum_T,T)] Sum_T = [x + y for x, y in zip(Sum_T, T)]
Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k] Sum_T = [x / R for x in Sum_T] # Experimental [Ti=k]
Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items Sum_T = [
x * 100 / (sum(Sum_T)) for x in Sum_T
] # Pourcentage de la repartition des items
print("Mean number of bins : {} (variance {})".format(mean(I), variance(I))) print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
for n in range(N): for n in range(N):
print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n]))) print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T))) print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
#Loi math # Loi math
for u in range(N): for u in range(N):
u=u+2 u = u + 2
T_maths.append(1/(factorial(u-1))-1/factorial(u)) T_maths.append(1 / (factorial(u - 1)) - 1 / factorial(u))
E=0 E = 0
sigma2=0 sigma2 = 0
# print(T_maths) # print(T_maths)
for p in range(len(T_maths)): for p in range(len(T_maths)):
E=E+(p+1)*T_maths[p] E = E + (p + 1) * T_maths[p]
sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1) sigma2 = ((T_maths[p] - E) ** 2) / (len(T_maths) - 1)
print("Mathematical values : Empiric mean T_{} : {} Variance {})".format(t_i, E, sqrt(sigma2))) print(
T_maths=[x*100 for x in T_maths] "Mathematical values : Empiric mean T_{} : {} Variance {})".format(
#Plotting t_i, E, sqrt(sigma2)
)
)
T_maths = [x * 100 for x in T_maths]
# Plotting
fig = plt.figure() fig = plt.figure()
#T plot # T plot
x = np.arange(N) x = np.arange(N)
print(x) print(x)
print(Sum_T) print(Sum_T)
ax = fig.add_subplot(221) ax = fig.add_subplot(221)
ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red') ax.bar(
ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,20), yticks=np.linspace(0, 20, 2)) x,
ax.set_ylabel('Items(n) in %') Sum_T,
ax.set_xlabel('Bins (1-{})'.format(N)) width=1,
ax.set_title('Items percentage for each bin and {} items (Number of items in each bin)'.format(P)) label="Empirical values",
ax.legend(loc='upper left',title='Legend') edgecolor="blue",
linewidth=0.7,
color="red",
)
ax.set(
xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 20), yticks=np.linspace(0, 20, 2)
)
ax.set_ylabel("Items(n) in %")
ax.set_xlabel("Bins (1-{})".format(N))
ax.set_title(
"Items percentage for each bin and {} items (Number of items in each bin)".format(
P
)
)
ax.legend(loc="upper left", title="Legend")
#Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items. # Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
print(len(Tk[t_i])) print(len(Tk[t_i]))
bx = fig.add_subplot(222) bx = fig.add_subplot(222)
bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red') bx.hist(
bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,len(Tk[t_i])), yticks=np.linspace(0, 1, 1)) Tk[t_i],
bx.set_ylabel('P(T{}=i)'.format(t_i)) bins=10,
bx.set_xlabel('Bins i=(1-{}) in %'.format(N)) width=1,
bx.set_title('T{} histogram for {} items (Number of items in each bin)'.format(t_i,P)) label="Empirical values",
bx.legend(loc='upper left',title='Legend') edgecolor="blue",
linewidth=0.7,
color="red",
)
bx.set(
xlim=(0, N),
xticks=np.arange(0, N),
ylim=(0, len(Tk[t_i])),
yticks=np.linspace(0, 1, 1),
)
bx.set_ylabel("P(T{}=i)".format(t_i))
bx.set_xlabel("Bins i=(1-{}) in %".format(N))
bx.set_title(
"T{} histogram for {} items (Number of items in each bin)".format(t_i, P)
)
bx.legend(loc="upper left", title="Legend")
#Loi mathematique # Loi mathematique
print(T_maths) print(T_maths)
cx = fig.add_subplot(224) cx = fig.add_subplot(224)
cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red') cx.bar(
cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,100), yticks=np.linspace(0, 100, 10)) x,
cx.set_ylabel('P(T{}=i)'.format(t_i)) T_maths,
cx.set_xlabel('Bins i=(1-{})'.format(N)) width=1,
cx.set_title('Theoretical T{} values in %'.format(t_i)) label="Theoretical values",
cx.legend(loc='upper left',title='Legend') edgecolor="blue",
linewidth=0.7,
color="red",
)
cx.set(
xlim=(0, N),
xticks=np.arange(0, N),
ylim=(0, 100),
yticks=np.linspace(0, 100, 10),
)
cx.set_ylabel("P(T{}=i)".format(t_i))
cx.set_xlabel("Bins i=(1-{})".format(N))
cx.set_title("Theoretical T{} values in %".format(t_i))
cx.legend(loc="upper left", title="Legend")
plt.show() plt.show()
# unused # unused
def basic_demo(): def basic_demo():
N = 10 ** 1 N = 10**1
sim = simulate_NFBP(N) sim = simulate_NFBP(N)
print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N)) print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 1): for j in range(sim["i"] + 1):
remplissage = floor(sim["R"][j] * 100) remplissage = floor(sim["R"][j] * 100)
print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j], print(
sim["V"][j])) "Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(
j, remplissage, sim["T"][j], sim["V"][j]
)
)
print() print()
stats_NFBP(10 ** 3, 10) stats_NFBP(10**3, 10)
N = 10 ** 1 N = 10**1
sim = simulate_NFDBP(N) sim = simulate_NFDBP(N)
print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N)) print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 1): for j in range(sim["i"] + 1):
remplissage = floor(sim["R"][j] * 100) remplissage = floor(sim["R"][j] * 100)
print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, print(
sim["T"][j], "Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(
sim["V"][j])) j, remplissage, sim["T"][j], sim["V"][j]
)
)
stats_NFBP_iter(10**3, 10) stats_NFBP_iter(10**3, 10)
print('\n\n') print("\n\n")
stats_NFDBP(10 ** 3, 10,1) stats_NFDBP(10**3, 10, 1)