def test_degenerated_grid():
""" test operators on grids with singular dimensions """
g1 = CartesianGrid([[0, 1]], 4)
g2 = CartesianGrid([[0, 1], [0, 0.1]], [4, 1], periodic=[False, True])
d = np.random.random(4)
v1 = g1.get_operator("laplace", bc="natural")(d)
v2 = g2.get_operator("laplace", bc="natural")(d.reshape(g2.shape))
assert v2.shape == g2.shape
np.testing.assert_allclose(v1.flat, v2.flat)
def test_rect_div_grad():
""" compare div grad to laplacian """
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16],
periodic=True)
x, y = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
arr = np.cos(x) + np.sin(y)
bcs = grid.get_boundary_conditions("natural")
laplace = grid.get_operator("laplace", bcs)
grad = grid.get_operator("gradient", bcs)
div = grid.get_operator("divergence", bcs.differentiated)
a = laplace(arr)
b = div(grad(arr))
np.testing.assert_allclose(a, -arr, rtol=0.05, atol=0.01)
np.testing.assert_allclose(b, -arr, rtol=0.05, atol=0.01)
def test_noise_scaling():
"""compare the noise strength (in terms of the spectral density of
two different noise sources that should be equivalent)"""
# create a grid
x, w = 2 + 10 * np.random.random(2)
size = np.random.randint(128, 256)
grid = CartesianGrid([[x, x + w]], size, periodic=True)
# colored noise
noise_colored = make_colored_noise(grid.shape, grid.discretization, exponent=2)
# divergence of white noise
shape = (grid.dim,) + grid.shape
div = grid.get_operator("divergence", bc="natural")
def noise_div():
return div(np.random.randn(*shape))
# calculate spectral densities of the two noises
result = []
for noise_func in [noise_colored, noise_div]:
def get_noise():
k, density = spectral_density(data=noise_func(), dx=grid.discretization)
assert k[0] == 0
assert density[0] == pytest.approx(0)
return np.log(density[1]) # log of spectral density
# average spectral density of longest length scale
mean = np.mean([get_noise() for _ in range(64)])
result.append(mean)
np.testing.assert_allclose(*result, rtol=0.5)
