def grad_linear_Ez(optimization, dJ, Ez, args):
"""gives the linear field gradient: partial J/ partial * E_lin dE_lin / deps"""
b_aj = -dJ(*args)
Ez_aj = adjoint_linear_Ez(optimization.simulation, b_aj)
EPSILON_0_ = EPSILON_0 * optimization.simulation.L0
omega = optimization.simulation.omega
dAdeps = optimization.design_region * omega**2 * EPSILON_0_
rho = optimization.simulation.rho
rho_t = rho2rhot(rho, optimization.W)
rho_b = rhot2rhob(rho_t, eta=optimization.eta, beta=optimization.beta)
eps_mat = (optimization.eps_m - 1)
filt_mat = drhot_drho(optimization.W)
proj_mat = drhob_drhot(rho_t, eta=optimization.eta, beta=optimization.beta)
Ez_vec = np.reshape(Ez, (-1, ))
dAdeps_vec = np.reshape(dAdeps, (-1, ))
dfdrho = eps_mat * filt_mat.multiply(Ez_vec * proj_mat * dAdeps_vec)
Ez_aj_vec = np.reshape(Ez_aj, (-1, ))
sensitivity_vec = dfdrho.dot(Ez_aj_vec)
return 1 * np.real(np.reshape(sensitivity_vec, rho.shape))
def grad_kerr_Ez(optimization, dJ, Ez_nl, args):
"""gives the linear field gradient: partial J/ partial * E_lin dE_lin / deps"""
b_aj = -dJ(*args)
Ez_aj = adjoint_kerr_Ez(optimization.simulation, b_aj)
optimization.simulation.compute_nl(Ez_nl)
EPSILON_0_ = EPSILON_0 * optimization.simulation.L0
omega = optimization.simulation.omega
dAdeps = optimization.design_region * omega**2 * EPSILON_0_
dAnldeps = dAdeps + optimization.design_region * omega**2 * EPSILON_0_ * optimization.simulation.dnl_deps
rho = optimization.simulation.rho
rho_t = rho2rhot(rho, optimization.W)
rho_b = rhot2rhob(rho_t, eta=optimization.eta, beta=optimization.beta)
eps_mat = (optimization.eps_m - 1)
filt_mat = drhot_drho(optimization.W)
proj_mat = drhob_drhot(rho_t, eta=optimization.eta, beta=optimization.beta)
Ez_vec = np.reshape(Ez_nl, (-1, ))
dfdrho = eps_mat * filt_mat.multiply(
Ez_vec * proj_mat * np.reshape(dAnldeps, (-1, )))
return 1 * np.real(
np.reshape(dfdrho.dot(np.reshape(Ez_aj, (-1, ))), rho.shape))
def grad_linear_Hy(optimization, dJ, Ez, args):
"""gives the linear field gradient: partial J/ partial * E_lin dE_lin / deps"""
# get the adjoint Ez corresponding to Hx
Dxb = optimization.simulation.derivs['Dxb']
partial = -dJ(*args)
partial_vec = partial.reshape((-1, ))
MU_0_ = MU_0 * optimization.simulation.L0
omega = optimization.simulation.omega
b_aj_vec = 1 / 1j / omega / MU_0_ * Dxb.T.dot(partial_vec)
b_aj = b_aj_vec.reshape(Ez.shape)
# rest is the same
Ez_aj = adjoint_linear_Ez(optimization.simulation, b_aj)
EPSILON_0_ = EPSILON_0 * optimization.simulation.L0
omega = optimization.simulation.omega
dAdeps = optimization.design_region * omega**2 * EPSILON_0_
rho = optimization.simulation.rho
rho_t = rho2rhot(rho, optimization.W)
rho_b = rhot2rhob(rho_t, eta=optimization.eta, beta=optimization.beta)
eps_mat = (optimization.eps_m - 1)
filt_mat = drhot_drho(optimization.W)
proj_mat = drhob_drhot(rho_t, eta=optimization.eta, beta=optimization.beta)
Ez_vec = np.reshape(Ez, (-1, ))
dAdeps_vec = np.reshape(dAdeps, (-1, ))
dfdrho = eps_mat * filt_mat.multiply(Ez_vec * proj_mat * dAdeps_vec)
Ez_aj_vec = np.reshape(Ez_aj, (-1, ))
sensitivity_vec = dfdrho.dot(Ez_aj_vec)
return 1 * np.real(np.reshape(sensitivity_vec, rho.shape))
def grad_kerr_Hy(optimization, dJ, Ez_nl, args):
"""gives the linear field gradient: partial J/ partial * E_lin dE_lin / deps"""
# get the adjoint source corresponding to Hy
Dxb = optimization.simulation.derivs['Dxb']
partial = -dJ(*args)
partial_vec = partial.reshape((-1, ))
MU_0_ = MU_0 * optimization.simulation.L0
omega = optimization.simulation.omega
b_aj_vec = 1 / 1j / omega / MU_0_ * Dxb.T.dot(partial_vec)
b_aj = b_aj_vec.reshape(Ez.shape)
# everything else is the same
Ez_aj = adjoint_kerr_Ez(optimization.simulation, b_aj)
optimization.simulation.compute_nl(Ez_nl)
EPSILON_0_ = EPSILON_0 * optimization.simulation.L0
omega = optimization.simulation.omega
dAdeps = optimization.design_region * omega**2 * EPSILON_0_
dAnldeps = dAdeps + optimization.design_region * omega**2 * EPSILON_0_ * optimization.simulation.dnl_deps
rho = optimization.simulation.rho
rho_t = rho2rhot(rho, optimization.W)
rho_b = rhot2rhob(rho_t, eta=optimization.eta, beta=optimization.beta)
eps_mat = (optimization.eps_m - 1)
filt_mat = drhot_drho(optimization.W)
proj_mat = drhob_drhot(rho_t, eta=optimization.eta, beta=optimization.beta)
Ez_vec = np.reshape(Ez_nl, (-1, ))
dfdrho = eps_mat * filt_mat.multiply(
Ez_vec * proj_mat * np.reshape(dAnldeps, (-1, )))
return 1 * np.real(
np.reshape(dfdrho.dot(np.reshape(Ez_aj, (-1, ))), rho.shape))
def grad_linear_Ey(optimization, dJ, Hz, args, averaging=False):
EPSILON_0_ = EPSILON_0 * optimization.simulation.L0
MU_0_ = MU_0 * optimization.simulation.L0
omega = optimization.simulation.omega
Dxb = optimization.simulation.derivs['Dxf']
Dyb = optimization.simulation.derivs['Dyf']
eps_tot = optimization.simulation.eps_r
M = eps_tot.size
if averaging:
eps_x = grid_average(EPSILON_0_ * (eps_tot), 'x')
vector_eps_x = eps_x.reshape((-1, ))
eps_y = grid_average(EPSILON_0_ * (eps_tot), 'y')
vector_eps_y = eps_y.reshape((-1, ))
else:
vector_eps_x = EPSILON_0_ * (eps_tot).reshape((-1, ))
vector_eps_y = EPSILON_0_ * (eps_tot).reshape((-1, ))
T_eps_x_inv = sp.spdiags(1 / vector_eps_x,
0,
M,
M,
format=DEFAULT_MATRIX_FORMAT)
T_eps_y_inv = sp.spdiags(1 / vector_eps_y,
0,
M,
M,
format=DEFAULT_MATRIX_FORMAT)
# get fields
Hz_vec = np.reshape(Hz, (-1, ))
Ex_vec = 1 / 1j / omega * T_eps_y_inv.dot(Dyb).dot(Hz_vec)
Ey_vec = -1 / 1j / omega * T_eps_x_inv.dot(Dxb).dot(Hz_vec)
partial = -dJ(*args)
partial_vec = partial.reshape((-1, ))
b_aj_vec = -1 / 1j / omega * T_eps_x_inv.dot(Dxb.T).dot(partial_vec)
b_aj = b_aj_vec.reshape(Hz.shape)
(Ex_aj, Ey_aj) = adjoint_linear_Hz(optimization.simulation,
b_aj,
averaging=averaging)
Ex_aj_vec = np.reshape(Ex_aj, (-1, )).T
Ey_aj_vec = np.reshape(Ey_aj, (-1, )).T
# set up filtering bits
rho = optimization.simulation.rho
rho_t = rho2rhot(rho, optimization.W)
rho_b = rhot2rhob(rho_t, eta=optimization.eta, beta=optimization.beta)
eps_mat = (optimization.eps_m - 1)
filt_mat = drhot_drho(optimization.W)
proj_mat = drhob_drhot(rho_t, eta=optimization.eta, beta=optimization.beta)
if averaging:
design_region_x = grid_average(optimization.design_region, 'x')
dAdeps_x = design_region_x * omega**2 * EPSILON_0_
design_region_y = grid_average(optimization.design_region, 'y')
dAdeps_y = design_region_y * omega**2 * EPSILON_0_
dAdeps_vec_x = np.reshape(dAdeps_x, (-1, ))
dAdeps_vec_y = np.reshape(dAdeps_y, (-1, ))
dfdrho_x = eps_mat * filt_mat.multiply(
Ex_vec * proj_mat * dAdeps_vec_x)
dfdrho_y = eps_mat * filt_mat.multiply(
Ey_vec * proj_mat * dAdeps_vec_x)
sensitivity_vec = dfdrho_x.dot(Ex_aj_vec) + dfdrho_y.dot(Ey_aj_vec)
else:
dAdeps = optimization.design_region * omega**2 * EPSILON_0_ # Note: physical constants go here if need be!
dAdeps_vec = np.reshape(dAdeps, (-1, ))
dfdrho_x = eps_mat * filt_mat.multiply(Ex_vec * proj_mat * dAdeps_vec)
dfdrho_y = eps_mat * filt_mat.multiply(Ey_vec * proj_mat * dAdeps_vec)
sensitivity_vec = dfdrho_x.dot(Ex_aj_vec) + dfdrho_y.dot(Ey_aj_vec)
return 1 * np.real(np.reshape(sensitivity_vec, rho.shape))