chore: lint

This commit is contained in:
Paul ALNET 2023-06-04 08:27:24 +02:00
parent 6bb38429d1
commit 316c910c3a

329
Probas.py
View file

@ -1,21 +1,22 @@
#!/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.
"""
i = 0 # Nombre de boites
i = 0 # Nombre de boites
R = [0] # Remplissage de la i-eme boite
T = [0] # Nombre de paquets de la i-eme boite
V = [0] # Taille du premier paquet de la i-eme boite
H = [] # Rang de la boite contenant le n-ieme paquet
H = [] # Rang de la boite contenant le n-ieme paquet
for n in range(N):
size = random()
if R[i] + size >= 1:
@ -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
@ -75,87 +71,122 @@ 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
x = np.arange(N)
# 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.
Next Fit Dual Bin Packing : bins should overflow
"""
i = 0 # Nombre de boites
i = 0 # Nombre de boites
R = [0] # Remplissage de la i-eme boite
T = [0] # Nombre de paquets de la i-eme boite
V = [0] # Taille du premier paquet de la i-eme boite
H = [] # Rang de la boite contenant le n-ieme paquet
H = [] # Rang de la boite contenant le n-ieme paquet
for n in range(N):
size = random()
if R[i] >= 1:
@ -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
x = np.arange(N)
# 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)