def test_curl_curl(U, x):
curl_curl_u = spherical_curl(*spherical_curl(*U, *x), *x)
grad_div_u = spherical_grad(spherical_div(*U, *x), *x)
vec_lap_u = spherical_vector_laplacian(*U, *x)
vec_delta = [
cc - (gd - vl)
for cc, gd, vl in zip(curl_curl_u, grad_div_u, vec_lap_u)
]
assert is_zero(vec_delta), vec_delta
def test_div_curl(U, x):
curl_u = spherical_curl(*U, *x)
div_curl_u = spherical_div(*curl_u, *x)
assert is_zero(div_curl_u), div_curl_u
def test_div_grad(u, x):
grad_u = spherical_grad(u, *x)
div_grad_u = spherical_div(*grad_u, *x)
lap_u = spherical_laplacian(u, *x)
delta = div_grad_u - lap_u
assert is_zero(delta), delta
r_max = 1.0
generator = GeneratorSpherical(n_points, r_min=r_min, r_max=r_max)
r, theta, phi = [t.reshape(-1, 1) for t in generator.get_examples()]
degrees = list(range(10))
harmoincs_fn = ZonalSphericalHarmonics(degrees=degrees)
F_r, F_theta, F_phi = [HarmonicsNN(degrees, harmoincs_fn) for _ in range(3)]
vector_u = (F_r(r, theta, phi), F_theta(r, theta, phi), F_phi(r, theta, phi))
f = HarmonicsNN(degrees, harmoincs_fn)
scalar_u = f(r, theta, phi)
curl = lambda a, b, c: spherical_curl(a, b, c, r, theta, phi)
grad = lambda a: spherical_grad(a, r, theta, phi)
div = lambda a, b, c: spherical_div(a, b, c, r, theta, phi)
lap = lambda a: spherical_laplacian(a, r, theta, phi)
vec_lap = lambda a, b, c: spherical_vector_laplacian(a, b, c, r, theta, phi)
def is_zero(t):
if isinstance(t, (tuple, list)):
for i in t:
if not is_zero(i):
return False
return True
elif isinstance(t, torch.Tensor):
return t.detach().cpu().max() < EPS
else:
raise ValueError(f"t must be list, tuple or tensor; got {type(t)}")