fdfd_tools/examples/test.py

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()