def test_Ez_reverse(self):
print('\ttesting reverse-mode Ez in FDFD')
f = fdfd_ez(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
Hx, Hy, Ez = f.solve(eps_r * self.source_ez)
return npa.sum(npa.square(npa.abs(Ez))) \
+ npa.sum(npa.square(npa.abs(Hx))) \
+ npa.sum(npa.square(npa.abs(Hy)))
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', grad_numerical)
self.check_gradient_error(grad_numerical, grad_autograd_rev)
def test_Ez_forward(self):
print('\ttesting forward-mode Ez in FDFD')
f = fdfd_ez(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
Hx, Hy, Ez = f.solve(c * self.eps_r * self.source_ez)
return npa.square(npa.abs(Ez)) \
+ npa.square(npa.abs(Hx)) \
+ npa.square(npa.abs(Hy))
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 setUp(self):
# basic simulation parameters
self.Nx = 100
self.Ny = 100
self.omega = 2 * np.pi * 200e12
self.dL = 5e-8
self.pml = [10, 10]
# sources (chosen to have objectives around 1)
self.source_amp_ez = 1e3
self.source_amp_hz = 1e3
self.source_ez = np.zeros((self.Nx, self.Ny))
self.source_ez[self.Nx // 2, self.Ny // 2] = self.source_amp_ez
# starting relative permittivity (random for debugging)
self.eps_lin = np.ones((self.Nx, self.Ny))
self.chi3 = 2000
self.eps_nl = lambda Ez: self.eps_lin + 3 * self.chi3 * np.square(
np.abs(Ez))
f = fdfd_ez(self.omega, self.dL, self.eps_lin, self.pml)
Hx, Hy, Ez = f.solve(self.source_ez)
self.Ez = Ez
eps_nl = lambda Ez: self.eps_lin + 3 * self.eps_lin * self.chi3 * npa.square(
npa.abs(Ez))
f_nl = fdfd_ez_nl(self.omega, self.dL, self.eps_nl, self.pml)
Hx_nl, Hy_nl, Ez_nl = f_nl.solve(self.source_ez)
self.Ez_nl = Ez_nl
