chore: lint
This commit is contained in:
Paul ALNET
parent
6bb38429d1
commit
316c910c3a
1 changed files with 213 additions and 132 deletions
317
Probas.py
317
Probas.py
|
|
@ -1,12 +1,13 @@
|
|||
#!/usr/bin/python3
|
||||
from random import random
|
||||
from math import floor, sqrt,factorial
|
||||
from math import floor, sqrt, factorial
|
||||
from statistics import mean, variance
|
||||
from matplotlib import pyplot as plt
|
||||
from pylab import *
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as pt
|
||||
|
||||
|
||||
def simulate_NFBP(N):
|
||||
"""
|
||||
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
|
||||
H.append(i)
|
||||
|
||||
return {
|
||||
"i": i,
|
||||
"R": R,
|
||||
"T": T,
|
||||
"V": V,
|
||||
"H": H
|
||||
}
|
||||
return {"i": i, "R": R, "T": T, "V": V, "H": H}
|
||||
|
||||
|
||||
# unused
|
||||
|
|
@ -61,12 +56,13 @@ def stats_NFBP(R, N):
|
|||
for n in range(N):
|
||||
print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
|
||||
|
||||
|
||||
def stats_NFBP_iter(R, N):
|
||||
"""
|
||||
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.
|
||||
"""
|
||||
P=R*N # Total number of items
|
||||
P = R * N # Total number of items
|
||||
print("## Running {} NFBP simulations with {} items".format(R, N))
|
||||
# number of bins
|
||||
ISum = 0
|
||||
|
|
@ -75,77 +71,112 @@ def stats_NFBP_iter(R, N):
|
|||
HSum = [0 for _ in range(N)]
|
||||
HSumVariance = [0 for _ in range(N)]
|
||||
# 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
|
||||
Sum_V=[0 for _ in range(N)]
|
||||
Sum_V = [0 for _ in range(N)]
|
||||
|
||||
for i in range(R):
|
||||
sim = simulate_NFBP(N)
|
||||
ISum += sim["i"]
|
||||
IVarianceSum += sim["i"]**2
|
||||
IVarianceSum += sim["i"] ** 2
|
||||
for n in range(N):
|
||||
HSum[n] += sim["H"][n]
|
||||
HSumVariance[n] += sim["H"][n]**2
|
||||
T=sim['T']
|
||||
V=sim['V']
|
||||
HSumVariance[n] += sim["H"][n] ** 2
|
||||
T = sim["T"]
|
||||
V = sim["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)
|
||||
V.append(0)
|
||||
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_T = [x + y for x, y in zip(Sum_T, T)]
|
||||
Sum_V = [x + y for x, y in zip(Sum_V, V)]
|
||||
|
||||
Sum_T=[x/R for x in Sum_T]
|
||||
Sum_V=[round(x/R,2) for x in Sum_V]
|
||||
#print(Sum_V)
|
||||
I = ISum/R
|
||||
IVariance = sqrt(IVarianceSum/(R-1) - I**2)
|
||||
print("Mean number of bins : {} (variance {})".format(I, IVariance),'\n')
|
||||
Sum_T = [x / R for x in Sum_T]
|
||||
Sum_V = [round(x / R, 2) for x in Sum_V]
|
||||
# print(Sum_V)
|
||||
I = ISum / R
|
||||
IVariance = sqrt(IVarianceSum / (R - 1) - I**2)
|
||||
print("Mean number of bins : {} (variance {})".format(I, IVariance), "\n")
|
||||
# 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)):
|
||||
Hn = HSum[n]/R # moyenne
|
||||
HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
|
||||
print("Index of bin containing the {}th item (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
|
||||
HSum=[x/R for x in HSum]
|
||||
Hn = HSum[n] / R # moyenne
|
||||
HVariance = sqrt(HSumVariance[n] / (R - 1) - Hn**2) # Variance
|
||||
print(
|
||||
"Index of bin containing the {}th item (H_{}) : {} (variance {})".format(
|
||||
n, n, Hn, HVariance
|
||||
)
|
||||
)
|
||||
HSum = [x / R for x in HSum]
|
||||
# print(HSum)
|
||||
#Plotting
|
||||
# Plotting
|
||||
fig = plt.figure()
|
||||
#T plot
|
||||
# T plot
|
||||
x = np.arange(N)
|
||||
# print(x)
|
||||
ax = fig.add_subplot(221)
|
||||
ax.bar(x,Sum_T, width=1,label='Empirical values', 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
|
||||
ax.bar(
|
||||
x,
|
||||
Sum_T,
|
||||
width=1,
|
||||
label="Empirical values",
|
||||
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
|
||||
bx = fig.add_subplot(222)
|
||||
bx.bar(x,Sum_V, width=1,label='Empirical values', 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
|
||||
#We will simulate this part for a asymptotic study
|
||||
bx.bar(
|
||||
x,
|
||||
Sum_V,
|
||||
width=1,
|
||||
label="Empirical values",
|
||||
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
|
||||
# We will simulate this part for a asymptotic study
|
||||
cx = fig.add_subplot(223)
|
||||
cx.bar(x,HSum, width=1,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)
|
||||
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')
|
||||
cx.bar(
|
||||
x,
|
||||
HSum,
|
||||
width=1,
|
||||
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)
|
||||
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()
|
||||
|
||||
|
||||
def simulate_NFDBP(N):
|
||||
"""
|
||||
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
|
||||
T[i] += 1
|
||||
|
||||
return {
|
||||
"i": i,
|
||||
"R": R,
|
||||
"T": T,
|
||||
"V": V,
|
||||
"H": H
|
||||
}
|
||||
return {"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...
|
||||
"""
|
||||
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 = []
|
||||
H = [[] for _ in range(N)] # List of empty lists
|
||||
T=[]
|
||||
Tk=[[] for _ in range(N)]
|
||||
Ti=[]
|
||||
T_maths=[]
|
||||
#First iteration to use zip after
|
||||
sim=simulate_NFDBP(N)
|
||||
Sum_T=[0 for _ in range(N)]
|
||||
T = []
|
||||
Tk = [[] for _ in range(N)]
|
||||
Ti = []
|
||||
T_maths = []
|
||||
# First iteration to use zip after
|
||||
sim = simulate_NFDBP(N)
|
||||
Sum_T = [0 for _ in range(N)]
|
||||
for i in range(R):
|
||||
sim = simulate_NFDBP(N)
|
||||
I.append(sim["i"])
|
||||
for k in range(N):
|
||||
T.append(0)
|
||||
T=sim["T"]
|
||||
T = sim["T"]
|
||||
for n in range(N):
|
||||
H[n].append(sim["H"][n])
|
||||
Tk[n].append(sim["T"][n])
|
||||
Ti.append(sim["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*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items
|
||||
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 * 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)))
|
||||
|
||||
for n in range(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)))
|
||||
#Loi math
|
||||
# Loi math
|
||||
for u in range(N):
|
||||
u=u+2
|
||||
T_maths.append(1/(factorial(u-1))-1/factorial(u))
|
||||
E=0
|
||||
sigma2=0
|
||||
u = u + 2
|
||||
T_maths.append(1 / (factorial(u - 1)) - 1 / factorial(u))
|
||||
E = 0
|
||||
sigma2 = 0
|
||||
# print(T_maths)
|
||||
for p in range(len(T_maths)):
|
||||
E=E+(p+1)*T_maths[p]
|
||||
sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1)
|
||||
print("Mathematical values : Empiric mean T_{} : {} Variance {})".format(t_i, E, sqrt(sigma2)))
|
||||
T_maths=[x*100 for x in T_maths]
|
||||
#Plotting
|
||||
E = E + (p + 1) * T_maths[p]
|
||||
sigma2 = ((T_maths[p] - E) ** 2) / (len(T_maths) - 1)
|
||||
print(
|
||||
"Mathematical values : Empiric mean T_{} : {} Variance {})".format(
|
||||
t_i, E, sqrt(sigma2)
|
||||
)
|
||||
)
|
||||
T_maths = [x * 100 for x in T_maths]
|
||||
# Plotting
|
||||
fig = plt.figure()
|
||||
#T plot
|
||||
# T plot
|
||||
x = np.arange(N)
|
||||
print(x)
|
||||
print(Sum_T)
|
||||
ax = fig.add_subplot(221)
|
||||
ax.bar(x,Sum_T, width=1,label='Empirical values', 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')
|
||||
ax.bar(
|
||||
x,
|
||||
Sum_T,
|
||||
width=1,
|
||||
label="Empirical values",
|
||||
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]))
|
||||
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.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')
|
||||
bx.hist(
|
||||
Tk[t_i],
|
||||
bins=10,
|
||||
width=1,
|
||||
label="Empirical values",
|
||||
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)
|
||||
cx = fig.add_subplot(224)
|
||||
cx.bar(x,T_maths, width=1,label='Theoretical values', 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')
|
||||
cx.bar(
|
||||
x,
|
||||
T_maths,
|
||||
width=1,
|
||||
label="Theoretical values",
|
||||
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()
|
||||
|
||||
|
||||
# unused
|
||||
def basic_demo():
|
||||
N = 10 ** 1
|
||||
N = 10**1
|
||||
sim = simulate_NFBP(N)
|
||||
|
||||
print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
|
||||
for j in range(sim["i"] + 1):
|
||||
remplissage = floor(sim["R"][j] * 100)
|
||||
print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j],
|
||||
sim["V"][j]))
|
||||
print(
|
||||
"Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(
|
||||
j, remplissage, sim["T"][j], sim["V"][j]
|
||||
)
|
||||
)
|
||||
|
||||
print()
|
||||
stats_NFBP(10 ** 3, 10)
|
||||
stats_NFBP(10**3, 10)
|
||||
|
||||
N = 10 ** 1
|
||||
N = 10**1
|
||||
sim = simulate_NFDBP(N)
|
||||
print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
|
||||
for j in range(sim["i"] + 1):
|
||||
remplissage = floor(sim["R"][j] * 100)
|
||||
print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage,
|
||||
sim["T"][j],
|
||||
sim["V"][j]))
|
||||
print(
|
||||
"Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(
|
||||
j, remplissage, sim["T"][j], sim["V"][j]
|
||||
)
|
||||
)
|
||||
|
||||
|
||||
stats_NFBP_iter(10**3, 10)
|
||||
print('\n\n')
|
||||
stats_NFDBP(10 ** 3, 10,1)
|
||||
print("\n\n")
|
||||
stats_NFDBP(10**3, 10, 1)
|
||||
|
|
|
|||
Loading…
Reference in a new issue