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Paul ALNET 2023-06-04 08:27:24 +02:00
parent 6bb38429d1
commit 316c910c3a
1 changed files with 213 additions and 132 deletions
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213
Probas.py
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@ -7,6 +7,7 @@ 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
@ -61,6 +56,7 @@ 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...
@ -86,10 +82,10 @@ def stats_NFBP_iter(R, N):
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)]
@ -100,14 +96,18 @@ def stats_NFBP_iter(R, N):
# 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(
"Index of bin containing the {}th item (H_{}) : {} (variance {})".format(
n, n, Hn, HVariance
)
)
HSum = [x / R for x in HSum] HSum = [x / R for x in HSum]
# print(HSum) # print(HSum)
# Plotting # Plotting
@ -116,36 +116,67 @@ def stats_NFBP_iter(R, N):
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",
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 # 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",
linewidth=0.7,
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 # H plot
# We will simulate this part for a asymptotic study # 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",
edgecolor="blue",
linewidth=0.7,
color="green",
)
cx.set(
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) xb = linspace(0, N, 10)
yb = Hn * xb / 10 yb = Hn * xb / 10
wb = HVariance * xb / 10 wb = HVariance * xb / 10
cx.plot(xb,yb,label='Theoretical E(Hn)',color='brown') cx.plot(xb, yb, label="Theoretical E(Hn)", color="brown")
cx.plot(xb,wb,label='Theoretical V(Hn)',color='purple') cx.plot(xb, wb, label="Theoretical V(Hn)", color="purple")
cx.legend(loc='upper left',title='Legend') 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.
@ -172,13 +203,7 @@ 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):
@ -186,6 +211,7 @@ 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))
# TODO comment this function
P = N * R # Total number of items 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
@ -208,7 +234,9 @@ def stats_NFDBP(R, N,t_i):
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)))
@ -225,7 +253,11 @@ def stats_NFDBP(R, N,t_i):
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(
"Mathematical values : Empiric mean T_{} : {} Variance {})".format(
t_i, E, sqrt(sigma2)
)
)
T_maths = [x * 100 for x in T_maths] T_maths = [x * 100 for x in T_maths]
# Plotting # Plotting
fig = plt.figure() fig = plt.figure()
@ -234,34 +266,77 @@ def stats_NFDBP(R, N,t_i):
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
@ -270,8 +345,11 @@ def basic_demo():
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)
@ -281,10 +359,13 @@ def basic_demo():
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)