def test_nonuniform_triangle_autocorrelation():
a = 0.7
b = 3
x = np.array([0, b])
t = NonuniformLineScan(x, a * x)
r, A = height_height_autocorrelation(t,
distances=np.linspace(-4, 4, 101))
assert_almost_equal(A[np.abs(r) < 1e-6][0], a ** 2 * b ** 3 / 3)
r3, A3 = height_height_autocorrelation(t.detrend(detrend_mode='center'),
distances=[0])
s, = t.physical_sizes
assert_almost_equal(A3[0], t.rms_height_from_profile() ** 2 * s)
x = np.array([0, 1., 1.3, 1.7, 2.0, 2.5, 3.0])
t = NonuniformLineScan(x, a * x)
r2, A2 = height_height_autocorrelation(t, distances=np.linspace(-4, 4,
101))
assert_array_almost_equal(A, A2)
r, A = height_height_autocorrelation(t.detrend(detrend_mode='center'),
distances=[0])
s, = t.physical_sizes
assert_almost_equal(A[0], t.rms_height_from_profile() ** 2 * s)
def test_nonuniform_impulse_autocorrelation():
a = 3
b = 2
x = np.array([0, a])
t = NonuniformLineScan(x, b * np.ones_like(x))
r, A = height_height_autocorrelation(t,
distances=np.linspace(-4, 4, 101))
A_ref = b ** 2 * (a - np.abs(r))
A_ref[A_ref < 0] = 0
assert_array_almost_equal(A, A_ref)
a = 3
b = 2
x = np.array([-a, 0, 1e-9, a - 1e-9, a, 2 * a])
y = np.zeros_like(x)
y[2] = b
y[3] = b
t = NonuniformLineScan(x, y)
r, A = height_height_autocorrelation(t,
distances=np.linspace(-4, 4, 101))
A_ref = b ** 2 * (a - np.abs(r))
A_ref[A_ref < 0] = 0
assert_array_almost_equal(A, A_ref)
t = t.detrend(detrend_mode='center')
r, A = height_height_autocorrelation(t,
distances=np.linspace(0, 10, 201))
s, = t.physical_sizes
assert_almost_equal(A[0], t.rms_height_from_profile() ** 2 * s)