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Probas.py Executable file → Normal file
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@ -1,16 +1,11 @@
#!/usr/bin/python3
from random import random from random import random
from math import floor, sqrt, factorial from math import floor, sqrt
from statistics import mean, variance from statistics import mean, variance
from matplotlib import pyplot as plt # from matplotlib import pyplot
from pylab import *
import numpy as np
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 boxes of random size.
""" """
i = 0 # Nombre de boites i = 0 # Nombre de boites
R = [0] # Remplissage de la i-eme boite R = [0] # Remplissage de la i-eme boite
@ -21,7 +16,7 @@ def simulate_NFBP(N):
size = random() size = random()
if R[i] + size >= 1: if R[i] + size >= 1:
# Il y n'y a plus de la place dans la boite pour le paquet. # Il y n'y a plus de la place dans la boite pour le paquet.
# On passe a la boite suivante (qu'on initialise) # On passe à la boite suivante (qu'on initialise)
i += 1 i += 1
R.append(0) R.append(0)
T.append(0) T.append(0)
@ -33,15 +28,20 @@ def simulate_NFBP(N):
V[i] = size V[i] = size
H.append(i) 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
def stats_NFBP(R, N): def stats_NFBP(R, N):
""" """
Runs R runs of NFBP (for N items) and studies distribution, variance, mean... Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
""" """
print("Running {} NFBP simulations with {} items".format(R, N)) print("Running {} NFBP simulations with {} packages".format(R, N))
I = [] I = []
H = [[] for _ in range(N)] # List of empty lists H = [[] for _ in range(N)] # List of empty lists
@ -51,29 +51,21 @@ def stats_NFBP(R, N):
for n in range(N): for n in range(N):
H[n].append(sim["H"][n]) H[n].append(sim["H"][n])
print("Mean number of bins : {} (variance {})".format(mean(I), variance(I))) print("Mean number of boxes : {} (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])))
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 packages) 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 print("Running {} NFBP simulations with {} packages".format(R, N))
print("## Running {} NFBP simulations with {} items".format(R, N))
# number of bins
ISum = 0 ISum = 0
IVarianceSum = 0 IVarianceSum = 0
# index of the bin containing the n-th item
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
Sum_T = [0 for _ in range(N)]
# size of the first item in the i-th bin
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)
@ -82,105 +74,19 @@ 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"]
V = sim["V"]
# ensure that T, V have the same length as Sum_T, Sum_V
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 / R for x in Sum_T]
Sum_V = [round(x / R, 2) for x in 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")
# TODO clarify line below
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]
# print(HSum)
# Plotting
fig = plt.figure()
# 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
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
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")
plt.show()
print("Mean number of boxes : {} (variance {})".format(I, IVariance))
for n in range(n):
Hn = HSum[n]/R
HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2)
print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
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 boxes 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 R = [0] # Remplissage de la i-eme boite
@ -189,185 +95,83 @@ def simulate_NFDBP(N):
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): for n in range(N):
size = random() size = random()
if R[i] >= 1: R[i] += size
T[i] += 1
if R[i] + size >= 1:
# Il y n'y a plus de la place dans la boite pour le paquet. # Il y n'y a plus de la place dans la boite pour le paquet.
# On passe a la boite suivante (qu'on initialise). # On passe à la boite suivante (qu'on initialise)
i += 1 i += 1
R.append(0) R.append(0)
T.append(0) T.append(0)
V.append(0) V.append(0)
if V[i] == 0: if V[i] == 0:
# C'est le premier paquet de la boite # C'est le premier paquet de la boite
V[i] = size V[i] = size
H.append(i) H.append(i)
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):
""" """
Runs R runs of NFDBP (for N items) and studies distribution, variance, mean... Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean...
""" """
print("## Running {} NFDBP simulations with {} items".format(R, N)) print("Running {} NFDBP simulations with {} packages".format(R, N))
# 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 = [] Tmean=[]
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): 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):
T.append(0)
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])
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
print("Mean number of bins : {} (variance {})".format(mean(I), variance(I))) for k in range(sim["i"]):
# for o in range(sim["i"]):
Tmean+=sim["T"]
print("Mean number of boxes : {} (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])))
# TODO variance for T_k doesn't see right for k in range(int(mean(I))+1):
print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T))) print(Tmean[7])
# Loi math # print("Mean T_{} : {} (variance {})".format(k, mean(Tmean[k]), variance(Tmean[k])))
for u in range(N):
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
fig = plt.figure()
# 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 right", title="Legend")
# TODO fix the graph below
# 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 right", title="Legend")
# 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 right", title="Legend")
plt.show()
# unused
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( print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j],
"Boite {} : Rempli a {} % avec {} paquets. Taille du premier paquet : {}".format( sim["V"][j]))
j, remplissage, sim["T"][j], sim["V"][j]
)
)
print() print()
stats_NFBP(10**3, 10) stats_NFBP(10 ** 4, 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( print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage,
"Boite {} : Rempli a {} % avec {} paquets. Taille du premier paquet : {}".format( sim["T"][j],
j, remplissage, sim["T"][j], sim["V"][j] sim["V"][j]))
)
)
print()
stats_NFDBP(10 ** 4, 10)
stats_NFBP_iter(10**6, 10)
#
# pyplot.plot([1, 2, 4, 4, 2, 1], color = 'red', linestyle = 'dashed', linewidth = 2,
# markerfacecolor = 'blue', markersize = 5)
# pyplot.ylim(0, 5)
# pyplot.title('Un exemple')
stats_NFBP_iter(10**3, 10)
print("\n\n")
stats_NFDBP(10**3, 10, 1)

2
latex/annex-performance.tex
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@ -1,5 +1,5 @@
For simplicity, we only include the script for the improved algorithm. For the For simplicity, we only include the script for the improved algorithm. For the
intuitive algorithm, simply replace the algorithm. The imports, timing and memory intuitive algorithm, simply replace the algorithm. The imports timing and memory
usage tracking code are nearly identical. usage tracking code are nearly identical.
\begin{lstlisting}[language=python] \begin{lstlisting}[language=python]

5
latex/annex-probabilistic.tex
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@ -1,5 +0,0 @@
Script should have been provided with report. % TODO
\lstinputlisting[language=Python]{../Probas.py}
% TODO include output example

6
latex/main.tex
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@ -113,12 +113,6 @@
\clearpage \clearpage
\subsection{Probabilistic analysis script}
\label{annex:probabilistic}
\input{annex-probabilistic}
\clearpage
% \includepdf[pages={1}, scale=0.96, % \includepdf[pages={1}, scale=0.96,
% pagecommand=\subsection{Questionnaire 1 : Sensibilisation à l’Hygiène et à la Sécurité}] % pagecommand=\subsection{Questionnaire 1 : Sensibilisation à l’Hygiène et à la Sécurité}]