def gaussian_elimination(coefficient_matrix, result_matrix):
augmented_matrix = coefficient_matrix.copy()
augmented_matrix.append_column(result_matrix.copy())
augmented_matrix = lu_decomposition(augmented_matrix).U
result_column_index = augmented_matrix.size.width;
solution_matrix = create_matrix(coefficient_matrix.size.height, 1)
# Backward substitution
for i in range(0, coefficient_matrix.size.height):
solution_index = augmented_matrix.size.height - i
right_side = augmented_matrix.get(solution_index, result_column_index)
left_side_coefficient = augmented_matrix.get(solution_index, solution_index)
subtraction = 0
for n in range(solution_index, coefficient_matrix.size.width):
subtraction += augmented_matrix.get(solution_index, n + 1) * solution_matrix.get(n + 1, 1)
solution = (right_side - subtraction) / left_side_coefficient
solution_matrix.set(solution_index, 1, solution)
return solution_matrix
def test_multiply_decomposed_values(self):
a = parse_matrix("2 12;1 4")
lu = lu_decomposition(a)
self.assertEqual(a, lu.L * lu.U)
def test_lower_triangular_matrix(self):
a = parse_matrix("1 4;2 12")
lu = lu_decomposition(a)
self.assertEqual(parse_matrix("1 0;0.5 1"), lu.L)
def test_upper_triangular_matrix(self):
a = parse_matrix("1 4;2 12")
lu = lu_decomposition(a)
self.assertEqual(parse_matrix("2 12;0 -2"), lu.U)
