def integrate_parabola():
v = lambda x: x * (x - 1)
n_1 = 2
n_2 = 100
tr_1 = trapezoidal(v, 2., 6, n_1)
rec_1 = rectangular(v, 2., 6, n_1)
tr_2 = trapezoidal(v, 2., 6, n_2)
rec_2 = rectangular(v, 2., 6, n_2)
error_2 = tr_1 - rec_1
error_100 = tr_2 - tr_1
print("error for 2 breaks: ", error_2)
print("error for 100 breaks", error_100)
def rectangular_test_func():
exact = 33.5
v = lambda x: 2 * x**3
n = 2
numerical = rectangular(v, 1., 3, n)
error = abs(exact - numerical)
print('error: ', error)
def rectangular_methods(f, a, b, n, rec):
if rec == 'right':
return right_rectangular_method(f, a, b, n)
elif rec == 'left':
return left_rectangular_method(f, a, b, n)
elif rec == 'mid':
return rectangular(f, a, b, n)
def test_rectangular_byhand():
expected = 38
v = lambda x: 2 * x**3
computed = rectangular(v, 1., 3, 2)
tol = 1E-15
rel_error = abs(expected - computed)
success = rel_error < tol
msg = "погрешность = {0} больше допуска = {1}".format(rel_error, tol)
assert success, msg
def test_rectangular_linear():
v = lambda x: 2
V = lambda x: 2 * x
a = 1.1
b = 2.9
expected = V(b) - V(a)
computed = rectangular(v, a, b, 2)
tol = 1E-15
rel_error = abs(expected - computed)
success = rel_error < tol
msg = "Погрешность: {0}".format(rel_error)
assert success, msg
def rectangular_convergence_rates(f, F, a, b, num_expected=14):
expected = F(b) - F(a)
n = zeros(num_expected, dtype=int)
E = zeros(num_expected)
r = zeros(num_expected)
for i in range(num_expected):
n[i] = 2**(i + 1)
computed = rectangular(f, a, b, n[i])
E[i] = abs((expected - computed) / expected)
if i > 0:
r_im1 = log(E[i] / E[i - 1]) / log(float(n[i] / n[i - 1]))
r[i - 1] = float('%.2f' % r_im1)
return r