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Beautiful graphs

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Clément Lacau 2023-06-03 22:57:02 +02:00
parent ce5b4e560c
commit 7804bbfc43
1 changed files with 72 additions and 53 deletions
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125
Probas.py
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@ -5,6 +5,7 @@ from statistics import mean, variance
from matplotlib import pyplot as plt from matplotlib import pyplot as plt
from pylab import * from pylab import *
import numpy as np import numpy as np
import matplotlib.pyplot as pt
def simulate_NFBP(N): def simulate_NFBP(N):
""" """
@ -70,9 +71,8 @@ def stats_NFBP_iter(R, N):
IVarianceSum = 0 IVarianceSum = 0
HSum = [0 for _ in range(N)] HSum = [0 for _ in range(N)]
HSumVariance = [0 for _ in range(N)] HSumVariance = [0 for _ in range(N)]
Sum_T=[0 for _ in range(10)] Sum_T=[0 for _ in range(N)]
Sum_V=[] Sum_V=[0 for _ in range(N)]
Sum_H=[]
for i in range(R): for i in range(R):
sim = simulate_NFBP(N) sim = simulate_NFBP(N)
ISum += sim["i"] ISum += sim["i"]
@ -81,54 +81,63 @@ def stats_NFBP_iter(R, 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'] T=sim['T']
for i in range(5): V=sim['V']
for i in range(N):
T.append(0) T.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_H=Sum_H+sim['H'] Sum_V=[x+y for x,y in zip(Sum_V,V)]
for k in range(sim['i']):
#we use round to approximate variations of continuous variable V #we use round to approximate variations of continuous variable V
Sum_V.append(round(sim['V'][k],2)) # Sum_V= round(sim['V'],2))
Sum_T=[x/R for x in Sum_T] Sum_T=[x/R for x in Sum_T]
print(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 boxes : {} (variance {})".format(I, IVariance),'\n') print("Mean number of boxes : {} (variance {})".format(I, IVariance),'\n')
print(" {} * {} iterations of T".format(R,N),'\n') print(" {} * {} iterations of T".format(R,N),'\n')
for n in range(N):
Hn = HSum[n]/R # moyenne
HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2) # Variance
print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
HSum=[x/R for x in HSum]
print(HSum)
#Plotting #Plotting
#matplotlib.stairs(Sum_T,bins=[0,1,2,3,4])
#ax.hist(Sum_T, bins=8, edgecolor='k', density=True, label='Valeurs empiriques')
#ax.set(xlim=(0, 8), xticks=np.arange(1, 8),
#ylim=(0, 500), yticks=np.linspace(0, 56, 9))
#plot:
#fig = plt.subplots()
fig = plt.figure() fig = plt.figure()
#T plot #T plot
x = np.arange(7) 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, edgecolor="white", linewidth=0.7) ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
# ax.hist(Sum_T, bins=6, linewidth=0.5, edgecolor="white", label='Empirical values') ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0,10), yticks=np.linspace(0, 10, 1)) ax.set_ylabel('Items')
ax.set_xlabel('Boxes (1-{})'.format(N))
ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P)) ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
ax.legend() ax.legend(loc='upper left',title='Legend')
#V plot #V plot
bx = fig.add_subplot(222) bx = fig.add_subplot(222)
bx.hist(Sum_V, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values') bx.bar(x,Sum_V, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='orange')
bx.set(xlim=(0, 1), xticks=np.arange(0, 1),ylim=(0, 1000), yticks=np.linspace(0, 1000, 9)) 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('Boxes (1-{})'.format(N))
bx.set_title('V histogram for {} packages (first package size of each box)'.format(P)) bx.set_title('V histogram for {} packages (first package size of each box)'.format(P))
bx.legend() bx.legend(loc='upper left',title='Legend')
#H plot #H plot
cx = fig.add_subplot(223) #We will simulate this part for a asymptotic study
cx.hist(Sum_H, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values') cx = fig.add_subplot(223)
cx.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0, 2000), yticks=np.linspace(0, 2000, 9)) 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('Box ranking of n-item')
cx.set_xlabel('n-item (1-{})'.format(N))
cx.set_title('H histogram for {} packages'.format(P)) cx.set_title('H histogram for {} packages'.format(P))
cx.legend() 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() plt.show()
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):
""" """
@ -165,7 +174,7 @@ def simulate_NFDBP(N):
} }
def stats_NFDBP(R, N): def stats_NFDBP(R, N,t_i):
""" """
Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean... Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean...
""" """
@ -173,9 +182,9 @@ def stats_NFDBP(R, N):
P=N*R P=N*R
I = [] I = []
H = [[] for _ in range(N)] # List of empty lists H = [[] for _ in range(N)] # List of empty lists
Tmean=[]
T=[] T=[]
Sum_T=[] Tk=[[] for _ in range(N)]
Ti=[]
#First iteration to use zip after #First iteration to use zip after
sim=simulate_NFDBP(N) sim=simulate_NFDBP(N)
Sum_T=sim["T"] Sum_T=sim["T"]
@ -184,37 +193,47 @@ def stats_NFDBP(R, N):
I.append(sim["i"]) I.append(sim["i"])
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])
T=sim["T"] T=sim["T"]
for k in range(10): Ti.append(sim["T"])
for k in range(N):
Sum_T.append(0) Sum_T.append(0)
for k in range(sim["i"]): T.append(0)
Tmean.append(T[k]) Sum_T=[x+y for x,y in zip(Sum_T,T)]
Sum_T=[x+y for x,y in zip(Sum_T,sim["T"])] Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k]
print(Sum_T) Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items
print(sum(Sum_T)) print(Tk)
print(P)
Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T]
print(Sum_T)
print("Mean number of boxes : {} (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])))
print("Mean T_{} : {} (variance {})".format(k, mean(Tmean), variance(Tmean))) print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
#Plotting #Plotting
fig, ax = plt.subplots() fig = plt.figure()
#T plot #T plot
x = 0.5 + np.arange(8) x = np.arange(N)
x=x.tolist()
print(type(x))
print(x) print(x)
ax.bar(x, Sum_T, width=1, edgecolor="white", linewidth=0.5) ax = fig.add_subplot(121)
ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0, 25), yticks=np.linspace(0, 25, 9)) ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
ax.set_title('Repartition of packets in each box percents for {} packages '.format(P)) ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
ax.legend() ax.set_ylabel('Items')
ax.set_xlabel('Boxes (1-{})'.format(N))
ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
ax.legend(loc='upper left',title='Legend')
plt.show() plt.show()
#Mathematical P(Ti=k) plot
x = np.arange(N)
print(x)
ax = fig.add_subplot(122)
ax.hist(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('Boxes (1-{})'.format(N))
ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
ax.legend(loc='upper left',title='Legend')
plt.show()
N = 10 ** 1 N = 10 ** 1
sim = simulate_NFBP(N) sim = simulate_NFBP(N)