def test_dirichlet_bvp_spherical():
r0, r1 = x0, x1
r2 = (r0 + r1) / 2
no_condition = NoCondition()
# B.C. for the interior boundary (r_min)
net_f = FCNN(2, 1)
f = lambda th, ph: no_condition.enforce(net_f, th, ph)
# B.C. for the exterior boundary (r_max)
net_g = FCNN(2, 1)
g = lambda th, ph: no_condition.enforce(net_g, th, ph)
condition = DirichletBVPSpherical(r_0=r0, f=f, r_1=r1, g=g)
net = FCNN(3, 1)
theta = torch.rand(N_SAMPLES, 1) * np.pi
phi = torch.rand(N_SAMPLES, 1) * 2 * np.pi
r = r0 * ones
assert all_close(condition.enforce(net, r, theta, phi),
f(theta, phi)), "inner Dirichlet BC not satisfied"
r = r1 * ones
assert all_close(condition.enforce(net, r, theta, phi),
g(theta, phi)), "inner Dirichlet BC not satisfied"
condition = DirichletBVPSpherical(r_0=r2, f=f)
r = r2 * ones
assert all_close(condition.enforce(net, r, theta, phi),
f(theta, phi)), "single ended BC not satisfied"
def test_dirichlet_bvp_spherical():
# B.C. for the interior boundary (r_min)
interior = nn.Linear(in_features=2, out_features=1, bias=True)
f = lambda theta, phi: interior(torch.cat([theta, phi], dim=1))
# B.C. for the exterior boundary (r_max)
exterior = nn.Linear(in_features=2, out_features=1, bias=True)
g = lambda theta, phi: exterior(torch.cat([theta, phi], dim=1))
bvp = DirichletBVPSpherical(r_0=0., f=f, r_1=1.0, g=g)
net = nn.Linear(in_features=3, out_features=1, bias=True)
theta = torch.rand(10, 1) * np.pi
phi = torch.rand(10, 1) * 2 * np.pi
r = torch.zeros_like(theta)
v0 = f(theta, phi).detach().cpu().numpy()
u0 = bvp.enforce(net, r, theta, phi).detach().cpu().numpy()
assert np.isclose(v0, u0,
atol=1.e-5).all(), f"Unmatched boundary {v0} != {u0}"
r = torch.ones_like(theta)
v1 = g(theta, phi).detach().cpu().numpy()
u1 = bvp.enforce(net, r, theta, phi).detach().cpu().numpy()
assert np.isclose(v1, u1,
atol=1.e-5).all(), f"Unmatched boundary {v1} != {u1}"
bvp_half = DirichletBVPSpherical(r_0=2., f=f)
r = torch.ones_like(theta) * 2.
v2 = f(theta, phi).detach().cpu().numpy()
u2 = bvp_half.enforce(net, r, theta, phi).detach().cpu().numpy()
assert np.isclose(v2, u2,
atol=1.e-5).all(), f"Unmatched boundary {v2} != {u2}"