meanas/examples/test.py
2016-05-30 22:30:45 -07:00

235 lines
7.7 KiB
Python

import numpy
from numpy.ctypeslib import ndpointer
import ctypes
# h5py used by (uncalled) h5_write(); not used in currently-called code
from fdfd_tools import vec, unvec, waveguide_mode
import fdfd_tools, fdfd_tools.functional, fdfd_tools.grid
import gridlock
from matplotlib import pyplot
__author__ = 'Jan Petykiewicz'
def complex_to_alternating(x: numpy.ndarray) -> numpy.ndarray:
stacked = numpy.vstack((numpy.real(x), numpy.imag(x)))
return stacked.T.astype(numpy.float64).flatten()
def solve_A(A, b: numpy.ndarray) -> numpy.ndarray:
A_vals = complex_to_alternating(A.data)
b_vals = complex_to_alternating(b)
x_vals = numpy.zeros_like(b_vals)
args = ['dummy',
'--solver', 'QMR',
'--maxiter', '40000',
'--atol', '1e-6',
'--verbose', '100']
argc = ctypes.c_int(len(args))
argv_arr_t = ctypes.c_char_p * len(args)
argv_arr = argv_arr_t()
argv_arr[:] = [s.encode('ascii') for s in args]
A_dim = ctypes.c_int(A.shape[0])
A_nnz = ctypes.c_int(A.nnz)
npdouble = ndpointer(ctypes.c_double)
npint = ndpointer(ctypes.c_int)
lib = ctypes.cdll.LoadLibrary('/home/jan/magma_solve/zsolve_shared.so')
c_solver = lib.zsolve
c_solver.argtypes = [ctypes.c_int, argv_arr_t,
ctypes.c_int, ctypes.c_int,
npdouble, npint, npint, npdouble, npdouble]
c_solver(argc, argv_arr, A_dim, A_nnz, A_vals,
A.indptr.astype(numpy.intc),
A.indices.astype(numpy.intc),
b_vals, x_vals)
x = (x_vals[::2] + 1j * x_vals[1::2]).flatten()
return x
def write_h5(filename, A, b):
import h5py
# dtype=np.dtype([('real', 'float64'), ('imag', 'float64')])
h5py.get_config().complex_names = ('real', 'imag')
with h5py.File(filename, 'w') as mat_file:
mat_file.create_group('/A')
mat_file['/A/ir'] = A.indices.astype(numpy.intc)
mat_file['/A/jc'] = A.indptr.astype(numpy.intc)
mat_file['/A/data'] = A.data
mat_file['/b'] = b
mat_file['/x'] = numpy.zeros_like(b)
def test0():
dx = 50 # discretization (nm/cell)
pml_thickness = 10 # (number of cells)
wl = 1550 # Excitation wavelength
omega = 2 * numpy.pi / wl
# Device design parameters
radii = (1, 0.6)
th = 220
center = [0, 0, 0]
# refractive indices
n_ring = numpy.sqrt(12.6) # ~Si
n_air = 4.0 # air
# Half-dimensions of the simulation grid
xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx
# Coordinates of the edges of the cells.
half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max]
edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
# #### Create the grid, mask, and draw the device ####
grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3)
grid.draw_cylinder(surface_normal=gridlock.Direction.z,
center=center,
radius=max(radii),
thickness=th,
eps=n_ring**2,
num_points=24)
grid.draw_cylinder(surface_normal=gridlock.Direction.z,
center=center,
radius=min(radii),
thickness=th*1.1,
eps=n_air ** 2,
num_points=24)
dx0_a = grid.dxyz
dx0_b = [grid.shifted_dxyz(which_shifts=a)[a] for a in range(3)]
dxes = [dx0_a, dx0_b]
for a in (0, 1, 2):
for p in (-1, 1):
dxes = fdfd_tools.grid.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega,
thickness=pml_thickness)
J = [numpy.zeros_like(grid.grids[0], dtype=complex) for _ in range(3)]
J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1e5
A = fdfd_tools.functional.e_full(omega, dxes, vec(grid.grids)).tocsr()
b = -1j * omega * vec(J)
x = solve_A(A, b)
E = unvec(x, grid.shape)
print('Norm of the residual is {}'.format(numpy.linalg.norm(A.dot(x) - b)/numpy.linalg.norm(b)))
pyplot.figure()
pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic')
pyplot.axis('equal')
pyplot.show()
def test1():
dx = 40 # discretization (nm/cell)
pml_thickness = 10 # (number of cells)
wl = 1550 # Excitation wavelength
omega = 2 * numpy.pi / wl
# Device design parameters
w = 600
th = 220
center = [0, 0, 0]
# refractive indices
n_wg = numpy.sqrt(12.6) # ~Si
n_air = 1.0 # air
# Half-dimensions of the simulation grid
xyz_max = numpy.array([0.8, 0.9, 0.6]) * 1000 + (pml_thickness + 2) * dx
# Coordinates of the edges of the cells.
half_edge_coords = [numpy.arange(dx/2, m + dx/2, step=dx) for m in xyz_max]
edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
# #### Create the grid and draw the device ####
grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3)
grid.draw_cuboid(center=center, dimensions=[8e3, w, th], eps=n_wg**2)
dx0_a = grid.dxyz
dx0_b = [grid.shifted_dxyz(which_shifts=a)[a] for a in range(3)]
dxes = [dx0_a, dx0_b]
for a in (0, 1, 2):
for p in (-1, 1):
dxes = fdfd_tools.grid.stretch_with_scpml(dxes,omega=omega, axis=a, polarity=p,
thickness=pml_thickness)
half_dims = numpy.array([10, 20, 15]) * dx
dims = [-half_dims, half_dims]
dims[1][0] = dims[0][0]
ind_dims = (grid.pos2ind(dims[0], which_shifts=None).astype(int),
grid.pos2ind(dims[1], which_shifts=None).astype(int))
wg_args = {
'omega': omega,
'slices': [slice(i, f+1) for i, f in zip(*ind_dims)],
'dxes': dxes,
'axis': 0,
'polarity': +1,
}
wg_results = waveguide_mode.solve_waveguide_mode(mode_number=0, **wg_args, epsilon=grid.grids)
J = waveguide_mode.compute_source(**wg_args, **wg_results)
H_overlap = waveguide_mode.compute_overlap_e(**wg_args, **wg_results)
A = fdfd_tools.operators.e_full(omega, dxes, vec(grid.grids)).tocsr()
b = -1j * omega * vec(J)
x = solve_A(A, b)
E = unvec(x, grid.shape)
print('Norm of the residual is ', numpy.linalg.norm(A @ x - b))
def pcolor(v):
vmax = numpy.max(numpy.abs(v))
pyplot.pcolor(v, cmap='seismic', vmin=-vmax, vmax=vmax)
pyplot.axis('equal')
pyplot.colorbar()
center = grid.pos2ind([0, 0, 0], None).astype(int)
pyplot.figure()
pyplot.subplot(2, 2, 1)
pcolor(numpy.real(E[1][center[0], :, :]))
pyplot.subplot(2, 2, 2)
pyplot.plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10))
pyplot.subplot(2, 2, 3)
pcolor(numpy.real(E[1][:, :, center[2]]))
pyplot.subplot(2, 2, 4)
def poyntings(E):
e = vec(E)
h = fdfd_tools.operators.e2h(omega, dxes) @ e
cross1 = fdfd_tools.operators.poynting_e_cross(e, dxes) @ h.conj()
cross2 = fdfd_tools.operators.poynting_h_cross(h.conj(), dxes) @ e
s1 = unvec(0.5 * numpy.real(cross1), grid.shape)
s2 = unvec(0.5 * numpy.real(-cross2), grid.shape)
return s1, s2
s1x, s2x = poyntings(E)
pyplot.plot(s1x[0].sum(axis=2).sum(axis=1))
pyplot.hold(True)
pyplot.plot(s2x[0].sum(axis=2).sum(axis=1))
pyplot.show()
q = []
for i in range(-5, 30):
H_rolled = [numpy.roll(h, i, axis=0) for h in H_overlap]
q += [numpy.abs(vec(E) @ vec(H_rolled))]
pyplot.figure()
pyplot.plot(q)
pyplot.title('Overlap with mode')
pyplot.show()
print('Average overlap with mode:', sum(q)/len(q))
if __name__ == '__main__':
# test0()
test1()