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lacau:iterative
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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 math import floor, sqrt, factorial
from math import floor, sqrt
from statistics import mean, variance
from matplotlib import pyplot as plt
from pylab import *
import numpy as np
import matplotlib.pyplot as pt
# from matplotlib import pyplot
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
R = [0] # Remplissage de la i-eme boite
@ -21,7 +16,7 @@ def simulate_NFBP(N):
size = random()
if R[i] + size >= 1:
# 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
R.append(0)
T.append(0)
@ -33,15 +28,20 @@ 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
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 = []
H = [[] for _ in range(N)] # List of empty lists
@ -51,136 +51,42 @@ def stats_NFBP(R, N):
for n in range(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):
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...
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.
"""
P = R * N # Total number of items
print("## Running {} NFBP simulations with {} items".format(R, N))
# number of bins
print("Running {} NFBP simulations with {} packages".format(R, N))
ISum = 0
IVarianceSum = 0
# index of the bin containing the n-th item
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)]
# size of the first item in the i-th bin
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"]
# 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)]
HSumVariance[n] += sim["H"][n]**2
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")
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()
I = ISum/R
IVariance = sqrt(IVarianceSum/(R-1) - I**2)
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):
"""
Tries to simulate T_i, V_i and H_n for N items of random size.
Next Fit Dual Bin Packing : bins should overflow
Tries to simulate T_i, V_i and H_n for N boxes of random size.
"""
i = 0 # Nombre de boites
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
for n in range(N):
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.
# On passe a la boite suivante (qu'on initialise).
# On passe à la boite suivante (qu'on initialise)
i += 1
R.append(0)
T.append(0)
V.append(0)
if V[i] == 0:
# C'est le premier paquet de la boite
V[i] = size
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))
# TODO comment this function
P = N * R # Total number of items
print("Running {} NFDBP simulations with {} packages".format(R, N))
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)]
Tmean=[]
for i in range(R):
sim = simulate_NFDBP(N)
I.append(sim["i"])
for k in range(N):
T.append(0)
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
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):
print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
# TODO variance for T_k doesn't see right
print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
# Loi math
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")
for k in range(int(mean(I))+1):
print(Tmean[7])
# print("Mean T_{} : {} (variance {})".format(k, mean(Tmean[k]), variance(Tmean[k])))
# 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")
N = 10 ** 1
sim = simulate_NFBP(N)
# 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
sim = simulate_NFBP(N)
print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 1):
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 a {} % 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)
print()
stats_NFBP(10 ** 4, 10)
N = 10**1
sim = simulate_NFDBP(N)
print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
for j in range(sim["i"] + 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 a {} % 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_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
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.
\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
View file

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