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_power_spectrum_from_profile(self):
#
# this test was added, because there were issues calling
# power spectrum 1D with a window given
#
t = NonuniformLineScan(x=[1, 2, 3, 4], y=[2, 4, 6, 8])
q1, C1 = t.power_spectrum_from_profile(window='hann')
q1, C1 = t.detrend('center').power_spectrum_from_profile(window='hann')
q1, C1 = t.detrend('center').power_spectrum_from_profile()
q1, C1 = t.detrend('height').power_spectrum_from_profile(window='hann')
q1, C1 = t.detrend('height').power_spectrum_from_profile()
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)
def test_nonuniform3(self):
x = np.array((1, 2, 3, 4))
y = -2 * x
surf = NonuniformLineScan(x, y)
self.assertFalse(surf.is_uniform)
self.assertEqual(surf.dim, 1)
der = surf.derivative(n=1)
assert_array_equal(der, [-2, -2, -2])
der = surf.derivative(n=2)
assert_array_equal(der, [0, 0])
#
# Similar with detrend which substracts mean value
#
surf2 = surf.detrend(detrend_mode='center')
self.assertFalse(surf2.is_uniform)
self.assertEqual(surf.dim, 1)
der = surf2.derivative(n=1)
assert_array_equal(der, [-2, -2, -2])
#
# Similar with detrend which eliminates slope
#
surf3 = surf.detrend(detrend_mode='height')
self.assertFalse(surf3.is_uniform)
self.assertEqual(surf.dim, 1)
der = surf3.derivative(n=1)
np.testing.assert_allclose(der, [0, 0, 0], atol=1e-14)
np.testing.assert_allclose(surf3.heights(),
np.zeros(y.shape),
atol=1e-14)
p = surf3.positions_and_heights()
assert_array_equal(p[0], x)
np.testing.assert_allclose(p[1], np.zeros(y.shape), atol=1e-14)
def test_nonuniform_curvatures(self):
radius = 400.
center = 50.
# generate a nonregular monotically increasing sery of x
xs = np.cumsum(np.random.lognormal(size=20))
xs /= np.max(xs)
xs *= 80.
heights = 1 / (2 * radius) * (xs - center) ** 2
surface = NonuniformLineScan(xs, heights)
detrended = surface.detrend(detrend_mode="curvature")
self.assertAlmostEqual(abs(detrended.curvatures[0]), 1 / radius)
def test_nonuniform_quadratic(self):
x = np.linspace(0, 10, 11) ** 1.3
a = 1.2
b = 1.8
c = 0.3
y = a + b * x + c * x * x / 2
surf = NonuniformLineScan(x, y)
self.assertAlmostEqual(surf.rms_curvature_from_profile(), c)
surf = surf.detrend(detrend_mode='height')
self.assertAlmostEqual(surf.mean(), 0.0)
surf.detrend_mode = 'curvature'
self.assertAlmostEqual(surf.mean(), 0.0)
self.assertAlmostEqual(surf.rms_slope_from_profile(), 0.0)
self.assertAlmostEqual(surf.rms_curvature_from_profile(), 0.0)
def test_nonuniform2(self):
x = np.array((1, 2, 3))
y = 2 * x
surf = NonuniformLineScan(x, y)
self.assertFalse(surf.is_uniform)
self.assertEqual(surf.dim, 1)
der = surf.derivative(n=1)
assert_array_equal(der, [2, 2])
der = surf.derivative(n=2)
assert_array_equal(der, [0])
surf = surf.detrend(detrend_mode='height')
self.assertFalse(surf.is_uniform)
self.assertEqual(surf.dim, 1)
der = surf.derivative(n=1)
assert_array_equal(der, [0, 0])
assert_array_equal(surf.heights(), np.zeros(y.shape))
p = surf.positions_and_heights()
assert_array_equal(p[0], x)
assert_array_equal(p[1], np.zeros(y.shape))