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