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lacau:iterative
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compare: lacau:8284d7bf03b4597a3cba6353c22372de6c7a3757
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lacau:iterative

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Probas.py
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@ -9,13 +9,13 @@ 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 packages 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
T = [0] # Nombre de paquets 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 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): for n in range(N):
size = random() size = random()
if R[i] + size >= 1: if R[i] + size >= 1:
@ -41,12 +41,11 @@ def simulate_NFBP(N):
} }
# 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
@ -56,29 +55,24 @@ 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 P=R*N
print("## Running {} NFBP simulations with {} items".format(R, N)) print("Running {} NFBP simulations with {} packages".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)] 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): for i in range(R):
sim = simulate_NFBP(N) sim = simulate_NFBP(N)
ISum += sim["i"] ISum += sim["i"]
@ -88,56 +82,55 @@ def stats_NFBP_iter(R, 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 for i in range(N):
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)]
Sum_V=[x+y for x,y in zip(Sum_V,V)] Sum_V=[x+y for x,y in zip(Sum_V,V)]
#we use round to approximate variations of continuous variable V
# Sum_V= round(sim['V'],2))
Sum_T=[x/R for x in Sum_T] Sum_T=[x/R for x in Sum_T]
Sum_V=[round(x/R,2) for x in Sum_V] Sum_V=[round(x/R,2) for x in Sum_V]
#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 boxes : {} (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)): for n in range(N):
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 box containing the {}th package (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
fig = plt.figure() fig = plt.figure()
#T plot #T plot
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(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(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
ax.set_ylabel('Items') ax.set_ylabel('Items')
ax.set_xlabel('Bins (1-{})'.format(N)) ax.set_xlabel('Boxes (1-{})'.format(N))
ax.set_title('T histogram for {} items (Number of items in each bin)'.format(P)) ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
ax.legend(loc='upper left',title='Legend') 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(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(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_ylabel('First item size')
bx.set_xlabel('Bins (1-{})'.format(N)) bx.set_xlabel('Boxes (1-{})'.format(N))
bx.set_title('V histogram for {} items (first item size of each bin)'.format(P)) bx.set_title('V histogram for {} packages (first package size of each box)'.format(P))
bx.legend(loc='upper left',title='Legend') 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(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(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_ylabel('Box ranking of n-item')
cx.set_xlabel('n-item (1-{})'.format(N)) cx.set_xlabel('n-item (1-{})'.format(N))
cx.set_title('H histogram for {} items'.format(P)) cx.set_title('H histogram for {} packages'.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
@ -148,28 +141,29 @@ def stats_NFBP_iter(R, N):
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 packages 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
T = [0] # Nombre de paquets 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 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): 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 à 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)
# C'est le premier paquet de la boite V.append(0)
V.append(size)
H.append(i)
R[i] += size
T[i] += 1
if V[i] == 0:
# C'est le premier paquet de la boite
V[i] = size
H.append(i)
return { return {
"i": i, "i": i,
@ -182,10 +176,10 @@ def simulate_NFDBP(N):
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... 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))
P=N*R # Total number of items P=N*R
I = [] I = []
H = [[] for _ in range(N)] # List of empty lists H = [[] for _ in range(N)] # List of empty lists
T=[] T=[]
@ -209,7 +203,7 @@ def stats_NFDBP(R, N,t_i):
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 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])))
@ -220,13 +214,14 @@ def stats_NFDBP(R, N,t_i):
T_maths.append(1/(factorial(u-1))-1/factorial(u)) T_maths.append(1/(factorial(u-1))-1/factorial(u))
E=0 E=0
sigma2=0 sigma2=0
# print(T_maths) print("hep")
print(T_maths)
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()
#T plot #T plot
x = np.arange(N) x = np.arange(N)
@ -236,8 +231,8 @@ def stats_NFDBP(R, N,t_i):
ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red') 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(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_ylabel('Items(n) in %')
ax.set_xlabel('Bins (1-{})'.format(N)) ax.set_xlabel('Boxes (1-{})'.format(N))
ax.set_title('Items percentage for each bin and {} items (Number of items in each bin)'.format(P)) ax.set_title('Items percentage for each box and {} packages (Number of packages in each box)'.format(P))
ax.legend(loc='upper left',title='Legend') 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.
@ -246,8 +241,8 @@ def stats_NFDBP(R, N,t_i):
bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red') 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(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_ylabel('P(T{}=i)'.format(t_i))
bx.set_xlabel('Bins i=(1-{}) in %'.format(N)) bx.set_xlabel('Boxes i=(1-{}) in %'.format(N))
bx.set_title('T{} histogram for {} items (Number of items in each bin)'.format(t_i,P)) bx.set_title('T{} histogram for {} packages (Number of packages in each box)'.format(t_i,P))
bx.legend(loc='upper left',title='Legend') bx.legend(loc='upper left',title='Legend')
#Loi mathematique #Loi mathematique
@ -256,34 +251,32 @@ def stats_NFDBP(R, N,t_i):
cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red') 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(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_ylabel('P(T{}=i)'.format(t_i))
cx.set_xlabel('Bins i=(1-{})'.format(N)) cx.set_xlabel('Boxes i=(1-{})'.format(N))
cx.set_title('Theoretical T{} values in %'.format(t_i)) cx.set_title('Theoretical T{} values in %'.format(t_i))
cx.legend(loc='upper left',title='Legend') cx.legend(loc='upper left',title='Legend')
plt.show() plt.show()
# unused N = 10 ** 1
def basic_demo(): sim = simulate_NFBP(N)
N = 10 ** 1
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("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][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)
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])) sim["V"][j]))
print() print()
stats_NFBP(10 ** 3, 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):
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]))
stats_NFBP_iter(10**3, 10) stats_NFBP_iter(10**3, 10)
print('\n\n')
stats_NFDBP(10 ** 3, 10,1) stats_NFDBP(10 ** 3, 10,1)