Beautiful graphs

Probas.py

@@ -5,6 +5,7 @@ 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):
     """
@@ -70,9 +71,8 @@ def stats_NFBP_iter(R, N):
     IVarianceSum = 0
     HSum = [0 for _ in range(N)]
     HSumVariance = [0 for _ in range(N)]
-    Sum_T=[0 for _ in range(10)]
-    Sum_V=[]
-    Sum_H=[]
+    Sum_T=[0 for _ in range(N)]
+    Sum_V=[0 for _ in range(N)]
     for i in range(R):
         sim = simulate_NFBP(N)
         ISum += sim["i"]
@@ -81,54 +81,63 @@ def stats_NFBP_iter(R, N):
             HSum[n] += sim["H"][n]
             HSumVariance[n] += sim["H"][n]**2
         T=sim['T']
-        for i in range(5):
+        V=sim['V']
+        for i in range(N):
             T.append(0)
+            V.append(0)
         Sum_T=[x+y for x,y in zip(Sum_T,T)]
-        Sum_H=Sum_H+sim['H']
-        for k in range(sim['i']):
+        Sum_V=[x+y for x,y in zip(Sum_V,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]
-    print(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 boxes : {} (variance {})".format(I, IVariance),'\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
-    #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()
     #T plot
-    x =  np.arange(7)
+    x =  np.arange(N)
     print(x)
     ax = fig.add_subplot(221)
-    ax.bar(x,Sum_T, width=1, edgecolor="white", linewidth=0.7)
-  # ax.hist(Sum_T, bins=6, linewidth=0.5, edgecolor="white", label='Empirical values')
-    ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0,10), yticks=np.linspace(0, 10, 1))
+    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('Boxes (1-{})'.format(N))
     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
     bx = fig.add_subplot(222) 
-    bx.hist(Sum_V, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values')
-    bx.set(xlim=(0, 1), xticks=np.arange(0, 1),ylim=(0, 1000), yticks=np.linspace(0, 1000, 9))
+    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('Boxes (1-{})'.format(N))
     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
+    #We will simulate this part for a asymptotic study
     cx = fig.add_subplot(223)
-    cx.hist(Sum_H, bins=10, linewidth=0.5, edgecolor="white", label='Empirical values')
-    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.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() 
-    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):
     """
@@ -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...
     """
@@ -173,9 +182,9 @@ def stats_NFDBP(R, N):
     P=N*R
     I = []
     H = [[] for _ in range(N)]  # List of empty lists
-    Tmean=[]
     T=[]
-    Sum_T=[]
+    Tk=[[] for _ in range(N)]
+    Ti=[]
     #First iteration to use zip after
     sim=simulate_NFDBP(N)
     Sum_T=sim["T"]
@@ -184,37 +193,47 @@ def stats_NFDBP(R, N):
         I.append(sim["i"])
         for n in range(N):
             H[n].append(sim["H"][n])
+            Tk[n].append(sim["T"][n])
         T=sim["T"]
-        for k in range(10):
+        Ti.append(sim["T"])
+        for k in range(N):
             Sum_T.append(0)
-        for k in range(sim["i"]):
-                Tmean.append(T[k])
-        Sum_T=[x+y for x,y in zip(Sum_T,sim["T"])]
-    print(Sum_T)
-    print(sum(Sum_T))
-    print(P)
-    Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T]
-    print(Sum_T)
+            T.append(0)
+        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(Tk)
     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])))
-    print("Mean T_{} : {} (variance {})".format(k, mean(Tmean), variance(Tmean)))
+    print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
 
 #Plotting
-    fig, ax = plt.subplots()
+    fig = plt.figure()
     #T plot
-    x = 0.5 + np.arange(8)
-    x=x.tolist()
-    print(type(x))
+    x =  np.arange(N)
     print(x)
-    ax.bar(x, Sum_T, width=1, edgecolor="white", linewidth=0.5)
-    ax.set(xlim=(0, 10), xticks=np.arange(0, 10),ylim=(0, 25), yticks=np.linspace(0, 25, 9))
-    ax.set_title('Repartition of packets in each box percents for {} packages '.format(P))
-    ax.legend()
+    ax = fig.add_subplot(121)
+    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('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()
 
-
+    #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
 sim = simulate_NFBP(N)