def test_gauss():
matrix = Matrix([[2, 5, 1], [-1, 2, -2], [6, 2, 1]])
free = [1, 2, 3]
true_solution = [12 / 9, 10 / 57, -65 / 57]
solution = get_solution(gauss(matrix, free))
assert list_round(solution) == list_round(true_solution)
def test_transcendental_tangent():
task = 'x ** 2 - 2'
task_section = (0, 8)
true_solution = 2**.5
solution = get_solution(transcendental.tangent(task, task_section))
assert round(float(solution), 8) == round(float(true_solution), 8)
def test_interpolation_canonical_polynomial():
x_values = [-1, 1, 5]
y_values = [4, -2, 10]
true_solution = []
solution = get_solution(
interpolation.canonical_polynomial(x_values, y_values))
assert true_solution == solution
def test_transcendental_dichotomy():
task = 'x ** 2 - 2'
task_section = (0, 8)
true_solution = 2**.5
solution = get_solution(
transcendental.dichotomy(task, task_section, level_of_details=2))
assert round(float(solution), 8) == round(float(true_solution), 8)
def test_triple_solve():
matrix = Matrix([[-34, -26, 0, 0, 0], [64, -124, -56, 0, 0],
[0, 94, -274, -86, 0], [0, 0, 124, -484, -116],
[0, 0, 0, 154, -754]])
free = [34, 38, 42, 46, 50]
true_solution = [-.6181818, -.4993007, -.2794706, -.1437131, -.0956655]
solution = get_solution(triple(matrix, free))
assert list_round(solution, 7) == list_round(true_solution, 7)
def test_sys_of_nonlinear_eq_linearization():
variables = ['x', 'y']
system = ['x ** 2 + y ** 2 - 4', 'x ** 2 - y']
init_approx = (2, 2)
true_solution = [1.2490080305, 1.5663342918]
solution = get_solution(
nonlinear.linearization(system, variables, init_approx, iterations=11))
solution = list(solution.values())
assert list_round(solution, 8) == list_round(true_solution, 8)
def test_second_problem_power_method():
matrix = Matrix([
[-12, 4, 8],
[4, 11, -6],
[8, -6, 2],
])
true_solution = -17
solution = get_solution(second_problem.power_method(matrix))
assert round(float(solution)) == true_solution
def test_second_problem_yakobi_rotation():
matrix = Matrix([
[17, 1, 1],
[1, 17, 2],
[1, 2, 4],
])
true_solution = [16.0349, 18.31907, 3.646025]
solution = get_solution(
second_problem.yakobi_rotation(matrix))['Собственные числа']
assert list_round(solution, 4) == list_round(true_solution, 4)
def test_first_problem_iteration_zeidel():
matrix = Matrix([
[20, 4, -8],
[-3, 15, 5],
[6, 3, -18],
])
free = [1, -2, 3]
true_solution = [-.0077778, -.0743447, -.18165]
solution = get_solution(
first_problem_iteration.zeidel(matrix, free, iterations=5))
assert list_round(solution, 7) == list_round(true_solution, 7)
def test_first_problem_iteration_simple():
matrix = Matrix([
[20, 4, -8],
[-3, 15, 5],
[6, 3, -18],
])
free = [1, -2, 3]
true_solution = [-.0077608, -.0743338, -.1816226]
solution = get_solution(
first_problem_iteration.simple(matrix, free, iterations=7))
assert list_round(solution, 7) == list_round(true_solution, 7)
def test_transcendental_iterations():
task = 'x ** 3 - x ** 2 + x - 5'
task_section = (8, 8)
true_solution = 1.8814850755
solution = get_solution(
transcendental.iterations(task,
task_section,
level_of_details=2,
iterations=8,
accuracy_order=1))
assert round(float(solution), 8) == round(float(true_solution), 8)