def mapping(x, filter_radius, eta, beta):
filtered_field = mpa.conic_filter(x, filter_radius, design_shape.x,
design_shape.y, design_region_resolution)
projected_field = mpa.tanh_projection(filtered_field, beta, eta)
return projected_field.flatten()
def test_offdiagonal(self):
print("*** TESTING OFFDIAGONAL COMPONENTS ***")
filt = lambda x: mpa.conic_filter(x.reshape(
(Nx, Ny)), 0.25, design_region_size.x, design_region_size.y,
design_region_resolution).flatten()
## test the single frequency and multi frequency case
for frequencies in [[fcen], [1 / 1.58, fcen, 1 / 1.53]]:
## compute gradient using adjoint solver
adjsol_obj, adjsol_grad = adjoint_solver(filt(p),
MonitorObject.EIGENMODE,
frequencies, sapphire)
## backpropagate the gradient
if len(frequencies) > 1:
bp_adjsol_grad = np.zeros(adjsol_grad.shape)
for i in range(len(frequencies)):
bp_adjsol_grad[:, i] = tensor_jacobian_product(filt, 0)(
p, adjsol_grad[:, i])
else:
bp_adjsol_grad = tensor_jacobian_product(filt, 0)(p,
adjsol_grad)
## compute unperturbed S12
S12_unperturbed = forward_simulation(filt(p),
MonitorObject.EIGENMODE,
frequencies, sapphire)
## compare objective results
print(
"S12 -- adjoint solver: {}, traditional simulation: {}".format(
adjsol_obj, S12_unperturbed))
self.assertClose(adjsol_obj, S12_unperturbed, epsilon=1e-6)
## compute perturbed S12
S12_perturbed = forward_simulation(filt(p + dp),
MonitorObject.EIGENMODE,
frequencies, sapphire)
## compare gradients
if bp_adjsol_grad.ndim < 2:
bp_adjsol_grad = np.expand_dims(bp_adjsol_grad, axis=1)
adj_scale = (dp[None, :] @ bp_adjsol_grad).flatten()
fd_grad = S12_perturbed - S12_unperturbed
print(
"Directional derivative -- adjoint solver: {}, FD: {}".format(
adj_scale, fd_grad))
tol = 0.1 if mp.is_single_precision() else 0.04
self.assertClose(adj_scale, fd_grad, epsilon=tol)