Blatt 3

Blatt3/README.md

+
+
+Ergebnis:  
+![Plot](Diagramm.png)
+
+Alle Straßen außer x2 können in Einbahnstraßen umgewandelt werden, da der Fluss immer positiv bzw. negativ bleibt.
+Bei x2 wechselt der Fluss zweimal am Tag die Richtung (Vorzeichenwechsel).
+
+
+L: [  
+ [ 1.  0.  0.  0.]  
+ [-1.  1.  0.  0.]  
+ [ 0. -1.  1.  0.]  
+ [ 0.  2.  0.  1.]]
+
+U: [  
+ [-1  0  0  0]  
+ [ 0 -1  0  0]  
+ [-1  1 -1  0]  
+ [ 2 -2  0  1]]
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Blatt3/verkehr.py

+import numpy as np
+from numpy import pi, sin
+import scipy.linalg
+import matplotlib.pyplot as plt
+
+A = np.array([  [-1, 0, 0, 0],
+                [ 1,-1, 0, 0],
+                [ 0, 1,-1, 0],
+                [ 0,-2, 0, 1]])
+
+L = np.identity(4)
+U = A
+
+param = np.array([1,1,-2])
+
+for i in range(len(A)):
+    U[1,i] += U[0,i]*param[0]
+    U[2,i] += U[0,i]*param[1]
+    U[3,i] += U[0,i]*param[2]
+
+L[1,0] = -1*param[0]
+L[2,1] = -1*param[1]
+L[3,1] = -1*param[2]
+
+print("L:")
+print(L)
+print("U:")
+print(U)
+
+
+
+x1 = []
+x2 = []
+x3 = []
+x4 = []
+time  = []
+
+for t in range(0, 24*60): # 1440 Minuten
+    t = t/60 # zu 24 Stunden
+    
+    zA = 610 - 100 * sin((pi / 12) * t    )
+    aA = 450 -  25 * sin((pi /  3) * t + 5)
+    zB = 400 -  20 * sin((pi /  3) * t - 1)
+    aB = 640 +  50 * sin((pi / 12) * t - 7)
+    zC = 600 +  10 * sin((pi /  6) * t + 4)
+    
+    b = np.array([aA-zA, aB-zB, -zC, 0])
+    
+    y = scipy.linalg.solve(L, b)
+    x = scipy.linalg.solve(U, y)
+    
+    x1.append(x[0])
+    x2.append(x[1])
+    x3.append(x[2])
+    x4.append(x[3])
+    time.append(t)
+
+
+
+fig, ax = plt.subplots()
+ax.plot(time, x1, label='x1')
+ax.plot(time, x2, label='x2')
+ax.plot(time, x3, label='x3')
+ax.plot(time, x4, label='x4')
+ax.plot([0,24], [0,0], label='Nulllinie', color='black', linewidth=0.5)
+ax.set_xlabel('Zeit [h]')
+ax.set_ylabel('Flussmenge')
+ax.legend()
+plt.show()
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