solved Tasks 2 + 3

Schenk_Brandenberger_S6_Aufg2.py

@@ -5,9 +5,7 @@ def switchRows(matrix, row1, row2):
     matrix[[row1, row2]] = matrix[[row2, row1]]
     return matrix
 
-
-
-def gaussAltorithmus(A, b):
+def Schenk_Brandenberger_S6_Aufg2(A, b):
 
     def calculateRow(A, b, row, column):
         b[row] = [b[row][0] - (A[row][column] / A[column][column]) * b[column][0]]
@@ -15,11 +13,11 @@ def gaussAltorithmus(A, b):
         return A, b
 
     # Erstelle obere Dreiecksmatrix
+    countRowSwitch = 0
     columnsToEdit = []
     for row in range(1, len(A)):
         columnsToEdit.append(row - 1)
         for column in columnsToEdit:
-            print("Zeile", row, "Spalte", column)
             if(A[row-1][column] == 0 and (row - 1 == column)):
                 rowToSwitch = row
                 if(row == 1):
@@ -30,10 +28,11 @@ def gaussAltorithmus(A, b):
                             return "Matrix ist nicht regulär!"
                 A = switchRows(A, row - 1, rowToSwitch)
                 b = switchRows(b, row - 1, rowToSwitch)
+                countRowSwitch += 1
             else:
                 A, b = calculateRow(A, b, row, column)
 
-            print("\nA\n", A, "\nb\n", b)
+    print("\nObere Dreiecksmatrix A:\n", A, "\nb:\n", b)
 
     # Rückwärtseinsetzen
     columnsToEdit = []
@@ -41,35 +40,40 @@ def gaussAltorithmus(A, b):
         columnsToEdit.append(row + 1)
         for column in columnsToEdit:
             A, b = calculateRow(A, b, row, column)
-            print(A)
-            print(b)
         row -= 1
-        print("\nA\n", A, "\nb\n", b)
+    print("\nA:\n", A, "\nb:\n", b)
 
+    det = 1
     result = []
     for i in range(len(A)):
         result.append(b[i][0] / A[i][i])
-    return result
+        det *= A[i][i]
+    if(countRowSwitch % 2 == 1):
+        det *= (-1)
+    return result, det
 
 
 
 if __name__ == '__main__':
-    # Beispiel aus Vorlesungsfolen:
-    A = np.array([[1.0, 5.0, 6.0],
-                  [7.0, 9.0, 6.0],
-                  [2.0, 3.0, 4.0]])
-    b = np.array([[29.0],
-                   [43.0],
-                   [20.0]])
+    # Beispiel 4.2 aus Vorlesungsfolen:
+    # A = np.array([[1.0, 5.0, 6.0],
+    #               [7.0, 9.0, 6.0],
+    #               [2.0, 3.0, 4.0]])
+    # b = np.array([[29.0],
+    #                [43.0],
+    #                [20.0]])
 
-    # A = np.array([[1.0, 1.5, 2.0],
-    #                [2.0, 3.0, 5.0],
-    #                [0.0, 1.0, 2.0]])
-    #
-    # b = np.array([[16.0],
-    #                [35.0],
-    #                [12.0]])
+    # Beispiel aus Aufgabe 1a
+    A = np.array([[1.0, 1.5, 2.0],
+                   [2.0, 3.0, 5.0],
+                   [0.0, 1.0, 2.0]])
 
-    result = gaussAltorithmus(A, b)
+    b = np.array([[16.0],
+                   [35.0],
+                   [12.0]])
+
+    result, det = Schenk_Brandenberger_S6_Aufg2(A, b)
+    print("Ergebnis:")
     for i in range(len(result)):
-        print("x" + str(i) + ": " + str(result[i]))
+        print("x" + str(i) + ": " + str(result[i]))
+    print("Determinante: " + str(det))

Schenk_Brandenberger_S6_Aufg3.py

@@ -0,0 +1,21 @@
+import numpy as np
+from Schenk_Brandenberger_S6_Aufg2 import *
+
+
+if __name__ == '__main__':
+    # Beispiel 4.1 + 4.3 aus den Vorlesungsfolien
+    A = np.array([[-1.0, 1.0, 1.0],
+                  [1.0, -3.0, -2.0],
+                  [5.0, 1.0, 4.0]])
+    b = np.array([[0.0],
+                   [5.0],
+                   [3.0]])
+    c = np.array([[13.0],
+                  [-32.0],
+                  [22.0]])
+
+    result, det = Schenk_Brandenberger_S6_Aufg2(A, c)
+    print("Ergebnis:")
+    for i in range(len(result)):
+        print("x" + str(i) + ": " + str(result[i]))
+    print("Determinante: " + str(det))