def test_grad_for_E(self):
print('\ttesting E fields in FDTD (forward mode)')
F = fdtd(self.eps_r, dL=self.dL, npml=self.pml)
def objective(c):
F = fdtd(c * self.eps_r, dL=self.dL, npml=self.pml)
S = 0.0
for t_index in range(self.steps):
fields = F.forward(Jx=self.gaussian(t_index))
S += fields['Ex'] + fields['Ey'] + fields['Ez']
return S
c0 = 2.0
jac_autograd_for = jacobian(objective, mode='forward')(c0)
jac_numerical = jacobian(objective, mode='numerical', step_size=DEPS)(c0)
if VERBOSE:
print('\tobjective function value: ', objective(self.eps_arr))
print('\tjacobian (auto): \n\t\t', jac_autograd_for)
print('\tjacobian (num): \n\t\t', jac_numerical)
self.check_gradient_error(jac_numerical, jac_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)
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 test_Ez_lin(self):
print('\ttesting linear Ez in FDFD')
f = fdfd_ez(self.omega, self.dL, self.eps_lin, self.pml)
def J_fdfd(eps_arr):
f.eps_r = eps_arr.reshape((self.Nx, self.Ny))
# set the source amplitude to the permittivity at that point
Hx, Hy, Ez = f.solve(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_lin)
grad_numerical = jacobian(J_fdfd, mode='numerical')(self.eps_lin)
if VERBOSE:
print('\tobjective function value: ', J_fdfd(self.eps_lin))
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_nl(self):
print('\ttesting reverse-mode nonlinear Ez in FDFD')
f = fdfd_ez_nl(self.omega, self.dL, self.eps_nl, self.pml)
Hx, Hy, Ez = f.solve(self.source_ez)
mod_strength = self.chi3 * np.max(np.square(np.abs(Ez)))
print('\t\tmodulation strength (chi3 * max(|E|^2)) = {}'.format(
mod_strength))
def J_fdfd(eps_arr):
eps_lin = eps_arr.reshape((self.Nx, self.Ny))
# construct nonlinear epsilon using autograd numpy wrapper
eps_nl = lambda Ez: eps_lin + 3 * eps_lin * self.chi3 * npa.square(
npa.abs(Ez))
# set the permittivity
f.eps_r = eps_nl
# set the source amplitude to the permittivity at that point
Hx, Hy, Ez = f.solve(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_lin)
grad_numerical = jacobian(J_fdfd, mode='numerical')(self.eps_lin)
if VERBOSE:
print('\tobjective function value: ', J_fdfd(self.eps_lin))
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_grad_rev_E(self):
print('\ttesting E fields in FDTD (reverse mode)')
F = fdtd(self.eps_r, dL=self.dL, npml=self.pml)
def objective(eps_arr):
F.eps_r = eps_arr.reshape((self.Nx, self.Ny, self.Nz))
S = 0.0
for t_index in range(self.steps):
fields = F.forward(Jz=self.gaussian(t_index))
S += npa.sum(fields['Ex'] + fields['Ey'] + fields['Ez'])
return S
jac_autograd_rev = jacobian(objective, mode='reverse')(self.eps_arr)
jac_numerical = jacobian(objective, mode='numerical', step_size=DEPS)(self.eps_arr)
if VERBOSE:
print('\tobjective function value: ', objective(self.eps_arr))
print('\tjacobian (auto): \n\t\t', jac_autograd_rev)
print('\tjacobian (num): \n\t\t', jac_numerical)
self.check_gradient_error(jac_numerical, jac_autograd_rev)
