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.make_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)
def test_colored_noise():
"""test the implementation of the colored noise"""
grid = UnitGrid([64, 64], periodic=True)
for exponent in [0, -1, 2]:
scale = np.random.uniform(1, 10)
noise = make_colored_noise(grid.shape, grid.discretization, exponent, scale)
x = noise()
assert (
stats.normaltest(x.flat).pvalue > 2e-5
), f"Colored noise with exp={exponent} is not normal distributed"