def test_Hz_forward(self):
print('\ttesting forward-mode Hz in FDFD')
f = fdfd_hz(self.omega, self.dL, self.eps_r, self.pml)
def J_fdfd(c):
# set the permittivity
f.eps_r = c * self.eps_r
# set the source amplitude to the permittivity at that point
Ex, Ey, Hz = f.solve(c * self.eps_r * self.source_hz)
return npa.square(npa.abs(Hz)) \
+ npa.square(npa.abs(Ex)) \
+ npa.square(npa.abs(Ey))
grad_autograd_for = jacobian(J_fdfd, mode='forward')(1.0)
grad_numerical = jacobian(J_fdfd, mode='numerical')(1.0)
if VERBOSE:
print('\tobjective function value: ', J_fdfd(1.0))
print('\tgrad (auto): \n\t\t', grad_autograd_for)
print('\tgrad (num): \n\t\t', grad_numerical)
self.check_gradient_error(grad_numerical, grad_autograd_for)
def test_Hz_reverse(self):
print('\ttesting reverse-mode Hz in FDFD')
f = fdfd_hz(self.omega, self.dL, self.eps_r, self.pml)
def J_fdfd(eps_arr):
eps_r = eps_arr.reshape((self.Nx, self.Ny))
# set the permittivity
f.eps_r = eps_r
# set the source amplitude to the permittivity at that point
Ex, Ey, Hz = f.solve(eps_r * self.source_hz, iterative=True)
return npa.sum(npa.square(npa.abs(Hz))) \
+ npa.sum(npa.square(npa.abs(Ex))) \
+ npa.sum(npa.square(npa.abs(Ey)))
grad_autograd_rev = jacobian(J_fdfd, mode='reverse')(self.eps_arr)
grad_numerical = jacobian(J_fdfd, mode='numerical')(self.eps_arr)
if VERBOSE:
print('\tobjective function value: ', J_fdfd(self.eps_arr))
print('\tgrad (auto): \n\t\t', grad_autograd_rev)
print('\tgrad (num): \n\t\t\n', grad_numerical)
self.check_gradient_error(grad_numerical, grad_autograd_rev)
omega = 2 * np.pi * 200e12
dL = 4e-8
eps_max = 2
npml = 10
spc = 10
L = 3e-6
Nx, Ny = 2*npml + 4*spc + int(L/dL), 2*npml + 4*spc + int(L/dL)
eps_r = np.ones((Nx, Ny))
# make source
source = np.zeros((Nx, Ny))
source[npml+spc, Ny//2] = 1
# make design region
box_region = np.zeros((Nx, Ny))
box_region[npml+2*spc:npml+2*spc+int(L/dL), npml+2*spc:npml+2*spc+int(L/dL)] = 1
probe = np.zeros((Nx, Ny), dtype=np.complex128)
probe[-npml-spc, Ny//2] = 1
F = fdfd_hz(omega, dL, eps_r, [npml, npml])
# define the gradient for autograd
grad_I = grad(intensity)
from scipy.optimize import minimize
bounds = [(1, eps_max) if box_region.flatten()[i] == 1 else (1,1) for i in range(eps_r.size)]
minimize(intensity, eps_r, args=(), method='L-BFGS-B', jac=grad_I,
bounds=bounds, tol=None, callback=None,
options={'disp': True, 'maxcor': 10, 'ftol': 2.220446049250313e-09, 'gtol': 1e-05, 'eps': 1e-08, 'maxfun': 15000, 'maxiter': 150, 'iprint': -1, 'maxls': 20})