solved Tasks 2 + 3

Schenk_Brandenberger_S6_Aufg2.py

@@ -0,0 +1,79 @@
+import numpy as np
+
+
+def switchRows(matrix, row1, row2):
+    matrix[[row1, row2]] = matrix[[row2, row1]]
+    return matrix
+
+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]]
+        A[row] = [(A[row][i] - (A[row][column] / A[column][column]) * A[column][i]) for i in range(len(A[row]))]
+        return A, b
+
+    # Erstelle obere Dreiecksmatrix
+    countRowSwitch = 0
+    columnsToEdit = []
+    for row in range(1, len(A)):
+        columnsToEdit.append(row - 1)
+        for column in columnsToEdit:
+            if(A[row-1][column] == 0 and (row - 1 == column)):
+                rowToSwitch = row
+                if(row == 1):
+                    while(A[rowToSwitch][column] == 0):
+                        if(len(A) > rowToSwitch + 1):
+                            rowToSwitch += 1
+                        else:
+                            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("\nObere Dreiecksmatrix A:\n", A, "\nb:\n", b)
+
+    # Rückwärtseinsetzen
+    columnsToEdit = []
+    for row in range((len(A) - 2), -1, -1):
+        columnsToEdit.append(row + 1)
+        for column in columnsToEdit:
+            A, b = calculateRow(A, b, row, column)
+        row -= 1
+    print("\nA:\n", A, "\nb:\n", b)
+
+    det = 1
+    result = []
+    for i in range(len(A)):
+        result.append(b[i][0] / A[i][i])
+        det *= A[i][i]
+    if(countRowSwitch % 2 == 1):
+        det *= (-1)
+    return result, det
+
+
+
+if __name__ == '__main__':
+    # 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]])
+
+    # 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]])
+
+    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("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))