added classes aufg3

Schenk_Brandenberger_S10_Aufg3.py

@@ -0,0 +1,66 @@
+import numpy as np
+
+
+def Single_Jacobi_Iteration(B, c, xn):
+    return B @ xn + c
+
+
+def Single_Gauss_Seidel_Iteration(B, c, xn):
+    return B @ xn + c
+
+
+def A_Priori_Estimation(B, x0, x1, tol):
+    return np.log((tol / np.linalg.norm((x1 - x0), np.inf) * (1 - np.linalg.norm(B, np.inf)))) / np.log(
+        np.linalg.norm(B, np.inf))
+
+
+def A_Posteriori_Estimation(B, xn, xn_minus_one):
+    return (np.linalg.norm(B, np.inf) / (1 - np.linalg.norm(B, np.inf))) * np.linalg.norm(xn - xn_minus_one)
+
+
+def Schenk_Brandenberger_S10_Aufg3a(A, b, x0, tol, opt):
+    A = A.astype("float64")
+    b = b.astype("float64")
+    x0 = x0.astype("float64")
+    x1 = np.copy(x0)
+    L = np.tril(A, k=-1)
+    D = np.diag(np.diag(A))
+    R = np.triu(A, k=1)
+    n = 1
+
+    if opt == 0:
+        B = -np.linalg.inv(D) @ (L + R)
+        c = np.linalg.inv(D) @ b
+        x1 = Single_Jacobi_Iteration(B, c, x0)
+    elif opt == 1:
+        B = -np.linalg.inv(D + L) @ R
+        c = np.linalg.inv(D + L) @ b
+        x1 = Single_Gauss_Seidel_Iteration(B, c, x0)
+    xn = np.copy(x1)
+    xn_minus_one = np.copy(x0)
+    # a-priori Abschätzung
+    n2 = A_Priori_Estimation(B, x0, x1, tol)
+
+    while tol < A_Posteriori_Estimation(B, xn, xn_minus_one):
+        xn_minus_one = np.copy(xn)
+        if opt == 0:
+            xn = Single_Jacobi_Iteration(B, c, xn)
+        elif opt == 1:
+            xn = Single_Gauss_Seidel_Iteration(B, c, xn)
+        n = n + 1
+    return (xn, n, n2)
+
+
+A = np.array([[8, 5, 2], [5, 9, 1], [4, 2, 7]])
+b = np.array([[19], [5], [34]])
+x0 = np.array([[1], [-1], [3]])
+opt = 1  # 0 is Jacobi; 1 is Gauss-Seidel
+
+[xn, n, n2] = Schenk_Brandenberger_S10_Aufg3a(A, b, x0, 0.0001, opt)
+
+print("Solution vector xn:")
+print(xn)
+print("Number of iterations:")
+print(n)
+print("Used steps with a priori:")
+print(n2)

Schenk_Brandenberger_S10_Aufg3b_3c.py

@@ -0,0 +1,77 @@
+import numpy as np
+import time
+from Schenk_Brandenberger_S10_Aufg3 import *
+from Gauss_Algorithm import *
+import matplotlib.pyplot as plt
+
+#3b
+dim = 3000
+A = np.diag( np.diag( np.ones( ( dim , dim ) )*4000 ) )+ np.ones( ( dim , dim ) )
+dum1 = np.arange( 1 , np.int32( dim /2+1) , dtype = np.float64 ).reshape( ( np.int32( dim / 2 ) , 1 ) )
+dum2 = np.arange( np.int32( dim / 2 ) ,0 , -1 , dtype=np.float64 ).reshape( ( np.int32( dim / 2 ) , 1 ) )
+x = np.append( dum1 , dum2 , axis=0)
+b = A@x
+x0 = np.zeros( ( dim , 1 ) )
+tol = 1e-4
+
+startLinalgSolve = time.time()
+x_linalg_solve = np.linalg.solve(A,b)
+stoppLinalgSolve = time.time()
+
+startJacobi = time.time()
+[x_jacobi, n, n2] = Schenk_Brandenberger_S10_Aufg3(A,b,x0,tol,0)
+stoppJacobi = time.time()
+
+startGaussSeidel = time.time()
+[x_gauss_seidel, n, n2] = Schenk_Brandenberger_S10_Aufg3(A,b,x0,tol,0)
+stoppGaussSeidel = time.time()
+
+startGauss = time.time()
+x_gauss = Witschi_Floian_S6_Aufg2(A,b)[2]
+stoppGauss = time.time()
+
+print("***********Time Estimation***********")
+print("Time for np.linalg.solve:")
+print(stoppLinalgSolve-startLinalgSolve)
+print("Time for Jacobi:")
+print(stoppJacobi-startJacobi)
+print("Time for Gauss-Seidel:")
+print(stoppGaussSeidel-startGaussSeidel)
+print("Time for Gauss:")
+print(stoppGauss-startGauss)
+
+
+#In this algorithm for Jacobi and Gauss-Seidel is the B calculated every single time
+""" Time for np.linalg.solve:
+0.6146464347839355
+Time for Jacobi:
+319.44120621681213
+Time for Gauss-Seidel:
+307.4256772994995
+Time for Gauss:
+95.12803220748901 """
+
+#In this algorithm for Jacobi and Gauss-Seidel is the B calculated one time
+""" Time for np.linalg.solve:
+0.5016989707946777
+Time for Jacobi:
+18.02965211868286
+Time for Gauss-Seidel:
+17.64187240600586
+Time for Gauss:
+105.31756782531738 """
+
+print(x_gauss)
+
+#3c
+#x_axis = np.array(["x0","x1","x2"])
+#plt.plot(x_axis, x_linalg_solve)
+x_axis = np.arange(dim)
+plt.plot(x_axis, x_gauss_seidel-x)
+plt.plot(x_axis, x_jacobi-x)
+plt.plot(x_axis, x_gauss-x)
+plt.plot(x_axis, x_linalg_solve-x)
+plt.legend(["Gauss Seidel", "Jacobi", "Gauss", "Linalg"])
+plt.show()
+
+#Das Gauss-Verfahren ist genauer wie das Jacobi und Gauss-Seidel Verfahren