def test_analytic():
nb_pts = 1488
s = 4 * np.pi
x = np.arange(nb_pts) * s / nb_pts
h = np.sin(x)
t1 = UniformLineScan(h, (s, ))
t2 = UniformLineScan(h, (s, ), periodic=True)
t3 = t1.to_nonuniform()
d1 = t1.derivative(1)
d2 = t2.derivative(1)
d3 = t3.derivative(1)
np.testing.assert_allclose(d1,
np.cos(x[:-1] + (x[1] - x[0]) / 2),
atol=1e-5)
np.testing.assert_allclose(d2, np.cos(x + (x[1] - x[0]) / 2), atol=1e-5)
np.testing.assert_allclose(d3,
np.cos(x[:-1] + (x[1] - x[0]) / 2),
atol=1e-5)
d1 = t1.derivative(2)
d2 = t2.derivative(2)
d3 = t3.derivative(2)
np.testing.assert_allclose(d1, -np.sin(x[:-2] + (x[1] - x[0])), atol=1e-5)
np.testing.assert_allclose(d2, -np.sin(x), atol=1e-5)
np.testing.assert_allclose(d3, -np.sin(x[:-2] + (x[1] - x[0])), atol=1e-5)
def test_scale_factor():
nx = 8
sx = 1
topography = fourier_synthesis((nx, ), (sx, ),
0.8,
rms_height=1.,
periodic=True)
topography1 = UniformLineScan(topography.heights()[::2], sx, periodic=True)
topography2 = UniformLineScan(topography.heights()[1::2],
sx,
periodic=True)
d1 = topography.derivative(1, scale_factor=1)
d2 = topography.derivative(1, scale_factor=np.uint32(2))
d3 = topography1.derivative(1, scale_factor=1)
d4 = topography2.derivative(1, scale_factor=1)
assert len(d2) == len(d1)
np.testing.assert_allclose(d3, d2[::2])
np.testing.assert_allclose(d4, d2[1::2])
topography = fourier_synthesis((nx, ), (sx, ),
0.8,
rms_height=1.,
periodic=False)
topography1 = UniformLineScan(topography.heights()[::2],
sx,
periodic=False)
topography2 = UniformLineScan(topography.heights()[1::2],
sx,
periodic=False)
d1, d2 = topography.derivative(1, scale_factor=[1, 2])
d3 = topography1.derivative(1, scale_factor=1)
d4 = topography2.derivative(1, scale_factor=1)
assert len(d2) == len(d1) - 1
np.testing.assert_allclose(d3, d2[::2])
np.testing.assert_allclose(d4, d2[1::2])
ny = 10
sy = 0.8
topography = fourier_synthesis((nx, ny), (sx, sy),
0.8,
rms_height=1.,
periodic=False)
dx, dy = topography.derivative(1, scale_factor=[1, 2, 4])
dx1, dx2, dx4 = dx
dy1, dy2, dy4 = dy
assert dx1.shape[0] == nx - 1
assert dx1.shape[1] == ny - 1
assert dy1.shape[0] == nx - 1
assert dy1.shape[1] == ny - 1
assert dx2.shape[0] == nx - 2
assert dx2.shape[1] == ny - 2
assert dy2.shape[0] == nx - 2
assert dy2.shape[1] == ny - 2
assert dx4.shape[0] == nx - 4
assert dx4.shape[1] == ny - 4
assert dy4.shape[0] == nx - 4
assert dy4.shape[1] == ny - 4
dx, dy = topography.derivative(1, scale_factor=[(1, 4), (2, 1), (4, 2)])
dxn1, dxn2, dxn4 = dx
dyn4, dyn1, dyn2 = dy
np.testing.assert_allclose(dxn1, dx1)
np.testing.assert_allclose(dyn1, dy1)
np.testing.assert_allclose(dxn2, dx2)
np.testing.assert_allclose(dyn2, dy2)
np.testing.assert_allclose(dxn4, dx4)
np.testing.assert_allclose(dyn4, dy4)