116 lines
3.6 KiB
Python
116 lines
3.6 KiB
Python
def Kuengjoe_S06_Aufg2(A, b, eps=1e-12):
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lenA = len(A)
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A_work = [row[:] for row in A]
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b_work = b[:]
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if any(len(row) != lenA for row in A_work):
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raise ValueError("A muss eine quadratische Matrix sein")
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if len(b_work) != lenA:
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raise ValueError("Länge von b muss mit der Anzahl der Zeilen von A übereinstimmen")
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det_sign = 1
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for k in range(lenA):
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pivot_row = max(range(k, lenA), key=lambda i: abs(A_work[i][k]))
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pivot = A_work[pivot_row][k]
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if abs(pivot) < eps:
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raise ValueError("Matrice singolare während der Pivotisierung")
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if pivot_row != k:
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A_work[k], A_work[pivot_row] = A_work[pivot_row], A_work[k]
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b_work[k], b_work[pivot_row] = b_work[pivot_row], b_work[k]
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det_sign *= -1
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for i in range(k + 1, lenA):
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factor = A_work[i][k] / A_work[k][k]
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A_work[i][k] = 0.0
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for j in range(k + 1, lenA):
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A_work[i][j] -= factor * A_work[k][j]
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b_work[i] -= factor * b_work[k]
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detA = det_sign
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for i in range(lenA):
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detA *= A_work[i][i]
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solution = [0.0] * lenA
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for i in reversed(range(lenA)):
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if abs(A_work[i][i]) < eps:
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raise ValueError("Matrice singolare während der Rückwärtseinsetzung")
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summ = sum(A_work[i][j] * solution[j] for j in range(i + 1, lenA))
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solution[i] = (b_work[i] - summ) / A_work[i][i]
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A_triangle = A_work
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return A_triangle, detA, solution
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if __name__ == "__main__":
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coefficient_matrix_A1 = [
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[4, -1, -5],
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[-12, 4, 17],
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[32, -10, -41],
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]
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rhs_A1_primary = [-5, 19, -39]
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rhs_A1_secondary = [6, -12, 48]
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coefficient_matrix_A2 = [
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[2, 7, 3],
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[-4, -10, 0],
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[12, 34, 9],
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]
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rhs_A2_primary = [25, -24, 107]
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rhs_A2_secondary = [5, -22, 42]
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coefficient_matrix_A3 = [
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[-2, 5, 4],
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[-14, 38, 22],
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[6, -9, -27],
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]
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rhs_A3_primary = [1, 40, 75]
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rhs_A3_secondary = [16, 82, -120]
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coefficient_matrix_A4 = [
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[-1, 2, 3, 2, 5, 4, 3, -1],
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[3, 4, 2, 1, 0, 2, 3, 8],
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[2, 7, 5, -1, 2, 1, 3, 5],
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[3, 1, 2, 6, -3, 7, 2, -2],
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[5, 2, 0, 8, 7, 6, 1, 3],
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[-1, 3, 2, 3, 5, 3, 1, 4],
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[8, 7, 3, 6, 4, 9, 7, 9],
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[-3, 14, -2, 1, 0, -2, 10, 5],
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]
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rhs_A4 = [-11, 103, 53, -20, 95, 78, 131, -26]
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A = [
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[2.0, -1.0, 1.0],
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[3.0, 3.0, 9.0],
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[3.0, 3.0, 5.0],
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]
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b = [2.0, -1.0, 4.0]
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U, detA, x = Kuengjoe_S06_Aufg2(A, b)
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print("U =", U)
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print("det(A) =", detA)
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print("x =", x)
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linear_systems_to_solve = [
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("A1_primary", coefficient_matrix_A1, rhs_A1_primary),
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("A1_secondary", coefficient_matrix_A1, rhs_A1_secondary),
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("A2_primary", coefficient_matrix_A2, rhs_A2_primary),
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("A2_secondary", coefficient_matrix_A2, rhs_A2_secondary),
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("A3_primary", coefficient_matrix_A3, rhs_A3_primary),
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("A3_secondary", coefficient_matrix_A3, rhs_A3_secondary),
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("A4", coefficient_matrix_A4, rhs_A4),
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]
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for system_label, matrix_A, vector_b in linear_systems_to_solve:
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upper_triangular_matrix_U, determinant_of_A, solution_vector_x = Kuengjoe_S06_Aufg2(
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[row[:] for row in matrix_A], # copia profonda – preserva i dati originali
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vector_b[:] # idem per il termine noto
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)
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print(f"{system_label}:")
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print(" U =", upper_triangular_matrix_U)
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print(" det(A) =", determinant_of_A)
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print(" x =", solution_vector_x)
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print() |