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solved Tasks 2 + 3

This commit is contained in:
schrom01 2022-11-10 21:35:17 +01:00
parent 3a52f4f220
commit 2c82034065
2 changed files with 50 additions and 25 deletions
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54
Schenk_Brandenberger_S6_Aufg2.py
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@ -5,9 +5,7 @@ def switchRows(matrix, row1, row2):
matrix[[row1, row2]] = matrix[[row2, row1]] matrix[[row1, row2]] = matrix[[row2, row1]]
return matrix return matrix
def Schenk_Brandenberger_S6_Aufg2(A, b):
def gaussAltorithmus(A, b):
def calculateRow(A, b, row, column): def calculateRow(A, b, row, column):
b[row] = [b[row][0] - (A[row][column] / A[column][column]) * b[column][0]] 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 return A, b
# Erstelle obere Dreiecksmatrix # Erstelle obere Dreiecksmatrix
countRowSwitch = 0
columnsToEdit = [] columnsToEdit = []
for row in range(1, len(A)): for row in range(1, len(A)):
columnsToEdit.append(row - 1) columnsToEdit.append(row - 1)
for column in columnsToEdit: for column in columnsToEdit:
print("Zeile", row, "Spalte", column)
if(A[row-1][column] == 0 and (row - 1 == column)): if(A[row-1][column] == 0 and (row - 1 == column)):
rowToSwitch = row rowToSwitch = row
if(row == 1): if(row == 1):
@ -30,10 +28,11 @@ def gaussAltorithmus(A, b):
return "Matrix ist nicht regulär!" return "Matrix ist nicht regulär!"
A = switchRows(A, row - 1, rowToSwitch) A = switchRows(A, row - 1, rowToSwitch)
b = switchRows(b, row - 1, rowToSwitch) b = switchRows(b, row - 1, rowToSwitch)
countRowSwitch += 1
else: else:
A, b = calculateRow(A, b, row, column) A, b = calculateRow(A, b, row, column)
print("\nA\n", A, "\nb\n", b) print("\nObere Dreiecksmatrix A:\n", A, "\nb:\n", b)
# Rückwärtseinsetzen # Rückwärtseinsetzen
columnsToEdit = [] columnsToEdit = []
@ -41,35 +40,40 @@ def gaussAltorithmus(A, b):
columnsToEdit.append(row + 1) columnsToEdit.append(row + 1)
for column in columnsToEdit: for column in columnsToEdit:
A, b = calculateRow(A, b, row, column) A, b = calculateRow(A, b, row, column)
print(A)
print(b)
row -= 1 row -= 1
print("\nA\n", A, "\nb\n", b) print("\nA:\n", A, "\nb:\n", b)
det = 1
result = [] result = []
for i in range(len(A)): for i in range(len(A)):
result.append(b[i][0] / A[i][i]) 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__': if __name__ == '__main__':
# Beispiel aus Vorlesungsfolen: # Beispiel 4.2 aus Vorlesungsfolen:
A = np.array([[1.0, 5.0, 6.0], # A = np.array([[1.0, 5.0, 6.0],
[7.0, 9.0, 6.0], # [7.0, 9.0, 6.0],
[2.0, 3.0, 4.0]]) # [2.0, 3.0, 4.0]])
b = np.array([[29.0], # b = np.array([[29.0],
[43.0], # [43.0],
[20.0]]) # [20.0]])
# A = np.array([[1.0, 1.5, 2.0], # Beispiel aus Aufgabe 1a
# [2.0, 3.0, 5.0], A = np.array([[1.0, 1.5, 2.0],
# [0.0, 1.0, 2.0]]) [2.0, 3.0, 5.0],
# [0.0, 1.0, 2.0]])
# b = np.array([[16.0],
# [35.0],
# [12.0]])
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)): for i in range(len(result)):
print("x" + str(i) + ": " + str(result[i])) print("x" + str(i) + ": " + str(result[i]))
print("Determinante: " + str(det))

21
Schenk_Brandenberger_S6_Aufg3.py
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@ -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))