2022-11-11 21:50:54 +01:00
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import numpy as np
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def switchRows(matrix, row1, row2):
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matrix[[row1, row2]] = matrix[[row2, row1]]
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return matrix
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def Schenk_Brandenberger_S6_Aufg2(A, b):
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def calculateRow(A, b, row, column):
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b[row] = [b[row][0] - (A[row][column] / A[column][column]) * b[column][0]]
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A[row] = [(A[row][i] - (A[row][column] / A[column][column]) * A[column][i]) for i in range(len(A[row]))]
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return A, b
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# Erstelle obere Dreiecksmatrix
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countRowSwitch = 0
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columnsToEdit = []
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for row in range(1, len(A)):
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columnsToEdit.append(row - 1)
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for column in columnsToEdit:
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if(A[row-1][column] == 0 and (row - 1 == column)):
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rowToSwitch = row
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if(row == 1):
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while(A[rowToSwitch][column] == 0):
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if(len(A) > rowToSwitch + 1):
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rowToSwitch += 1
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else:
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return "Matrix ist nicht regulär!"
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A = switchRows(A, row - 1, rowToSwitch)
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b = switchRows(b, row - 1, rowToSwitch)
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countRowSwitch += 1
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else:
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A, b = calculateRow(A, b, row, column)
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2022-11-14 23:51:31 +01:00
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#print("\nObere Dreiecksmatrix A:\n", A, "\nb:\n", b)
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2022-11-11 21:50:54 +01:00
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# Rückwärtseinsetzen
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columnsToEdit = []
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for row in range((len(A) - 2), -1, -1):
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columnsToEdit.append(row + 1)
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for column in columnsToEdit:
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A, b = calculateRow(A, b, row, column)
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row -= 1
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2022-11-14 23:51:31 +01:00
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#print("\nA:\n", A, "\nb:\n", b)
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2022-11-11 21:50:54 +01:00
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det = 1
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result = []
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for i in range(len(A)):
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result.append(b[i][0] / A[i][i])
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det *= A[i][i]
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if(countRowSwitch % 2 == 1):
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det *= (-1)
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return result, det
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if __name__ == '__main__':
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# Überprüfung Aufgabe 1a
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# A = np.array([[20000.0, 30000.0, 10000.0],
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# [10000.0, 17000.0, 6000.0],
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# [2000.0, 3000.0, 2000.0]])
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#
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# b = np.array([[5200000.0],
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# [3000000.0],
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# [760000.0]])
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# Überprüfung Aufgabe 1c
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A = np.array([[20000.0, 30000.0, 10000.0],
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[10000.0, 17000.0, 6000.0],
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[2000.0, 3000.0, 2000.0]])
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b = np.array([[5720000.0],
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[3300000.0],
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[836000.0]])
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result, det = Schenk_Brandenberger_S6_Aufg2(A, b)
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print("Ergebnis:")
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for i in range(len(result)):
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print("x" + str(i) + ": " + str(result[i]))
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print("Determinante: " + str(det))
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