231 lines
8.1 KiB
Python
231 lines
8.1 KiB
Python
"""
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Routines for creating normalized 2D lattices and common photonic crystal
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cavity designs.
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"""
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from typing import Sequence
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import numpy
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from numpy.typing import NDArray
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def triangular_lattice(
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dims: Sequence[int],
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asymmetrical: bool = False
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) -> NDArray[numpy.float64]:
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"""
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Return an ndarray of `[[x0, y0], [x1, y1], ...]` denoting lattice sites for
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a triangular lattice in 2D. The lattice will be centered around `(0, 0)`,
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unless `asymmetrical=True` in which case there will be extra holes in the +x
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direction.
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Args:
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dims: Number of lattice sites in the [x, y] directions.
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asymmetrical: If `True`, each row in x will contain the same number of
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lattice sites. If `False`, the structure is symmetrical
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around `(0, 0)`.
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Returns:
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`[[x0, y0], [x1, 1], ...]` denoting lattice sites.
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"""
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dims = numpy.asarray(dims, dtype=int)
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if asymmetrical:
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k = 0
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else:
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k = 1
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positions = []
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ymax = (dims[1] - 1)/2
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for j in numpy.linspace(-ymax, ymax, dims[0]):
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j_odd = numpy.floor(j).astype(int) % 2
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x_offset = j_odd * 0.5
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y_offset = j * numpy.sqrt(3)/2
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num_x = dims[0] - k * j_odd
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xmax = (dims[0] - 1)/2
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xs = numpy.linspace(-xmax, xmax - k * j_odd, num_x) + x_offset
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ys = numpy.full_like(xs, y_offset)
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positions += [numpy.vstack((xs, ys)).T]
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xy = numpy.vstack(tuple(positions))
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return xy[xy[:, 0].argsort(), ]
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def square_lattice(dims: Sequence[int]) -> NDArray[numpy.float64]:
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"""
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Return an ndarray of `[[x0, y0], [x1, y1], ...]` denoting lattice sites for
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a square lattice in 2D. The lattice will be centered around `(0, 0)`.
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Args:
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dims: Number of lattice sites in the [x, y] directions.
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Returns:
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`[[x0, y0], [x1, 1], ...]` denoting lattice sites.
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"""
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xs, ys = numpy.meshgrid(range(dims[0]), range(dims[1]), 'xy')
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xs -= dims[0]/2
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ys -= dims[1]/2
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xy = numpy.vstack((xs.flatten(), ys.flatten())).T
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return xy[xy[:, 0].argsort(), ]
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# ### Photonic crystal functions ###
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def nanobeam_holes(
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a_defect: float,
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num_defect_holes: int,
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num_mirror_holes: int
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) -> NDArray[numpy.float64]:
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"""
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Returns a list of `[[x0, r0], [x1, r1], ...]` of nanobeam hole positions and radii.
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Creates a region in which the lattice constant and radius are progressively
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(linearly) altered over `num_defect_holes` holes until they reach the value
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specified by `a_defect`, then symmetrically returned to a lattice constant and
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radius of 1, which is repeated `num_mirror_holes` times on each side.
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Args:
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a_defect: Minimum lattice constant for the defect, as a fraction of the
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mirror lattice constant (ie., for no defect, `a_defect = 1`).
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num_defect_holes: How many holes form the defect (per-side)
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num_mirror_holes: How many holes form the mirror (per-side)
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Returns:
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ndarray `[[x0, r0], [x1, r1], ...]` of nanobeam hole positions and radii.
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"""
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a_values = numpy.linspace(a_defect, 1, num_defect_holes, endpoint=False)
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xs = a_values.cumsum() - (a_values[0] / 2) # Later mirroring makes center distance 2x as long
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mirror_xs = numpy.arange(1, num_mirror_holes + 1) + xs[-1]
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mirror_rs = numpy.ones_like(mirror_xs)
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return numpy.vstack((numpy.hstack((-mirror_xs[::-1], -xs[::-1], xs, mirror_xs)),
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numpy.hstack((mirror_rs[::-1], a_values[::-1], a_values, mirror_rs)))).T
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def ln_defect(
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mirror_dims: Sequence[int],
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defect_length: int,
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) -> NDArray[numpy.float64]:
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"""
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N-hole defect in a triangular lattice.
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Args:
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mirror_dims: `[x, y]` mirror lengths (number of holes). Total number of holes
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is `2 * n + 1` in each direction.
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defect_length: Length of defect. Should be an odd number.
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Returns:
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`[[x0, y0], [x1, y1], ...]` for all the holes
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"""
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if defect_length % 2 != 1:
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raise Exception('defect_length must be odd!')
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p = triangular_lattice([2 * d + 1 for d in mirror_dims])
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half_length = numpy.floor(defect_length / 2)
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hole_nums = numpy.arange(-half_length, half_length + 1)
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holes_to_keep = numpy.in1d(p[:, 0], hole_nums, invert=True)
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return p[numpy.logical_or(holes_to_keep, p[:, 1] != 0), ]
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def ln_shift_defect(
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mirror_dims: Sequence[int],
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defect_length: int,
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shifts_a: Sequence[float] = (0.15, 0, 0.075),
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shifts_r: Sequence[float] = (1, 1, 1)
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) -> NDArray[numpy.float64]:
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"""
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N-hole defect with shifted holes (intended to give the mode a gaussian profile
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in real- and k-space so as to improve both Q and confinement). Holes along the
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defect line are shifted and altered according to the `shifts_*` parameters.
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Args:
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mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
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is `2 * n + 1` in each direction.
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defect_length: Length of defect. Should be an odd number.
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shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line
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shifts_r: Factor to multiply the radius by. Should match length of `shifts_a`.
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Returns:
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`[[x0, y0, r0], [x1, y1, r1], ...]` for all the holes
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"""
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xy = ln_defect(mirror_dims, defect_length)
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# Add column for radius
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xyr = numpy.hstack((xy, numpy.ones((xy.shape[0], 1))))
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# Shift holes
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assert len(shifts_a) == len(shifts_r)
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x_removed = numpy.floor(defect_length / 2)
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for ind in range(len(shifts_a)):
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for sign in (-1, 1):
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x_val = sign * (x_removed + ind + 1)
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which = numpy.logical_and(xyr[:, 0] == x_val, xyr[:, 1] == 0)
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xyr[which, ] = (x_val + numpy.sign(x_val) * shifts_a[ind], 0, shifts_r[ind])
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return xyr
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def r6_defect(
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mirror_dims: Sequence[int],
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) -> NDArray[numpy.float64]:
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"""
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R6 defect in a triangular lattice.
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Args:
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mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
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is `2 * n + 1` in each direction.
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Returns:
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`[[x0, y0], [x1, y1], ...]` specifying hole centers.
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"""
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xy = triangular_lattice([2 * d + 1 for d in mirror_dims])
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rem_holes_plus = numpy.array([[1, 0],
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[0.5, +numpy.sqrt(3)/2],
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[0.5, -numpy.sqrt(3)/2]])
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rem_holes = numpy.vstack((rem_holes_plus, -rem_holes_plus))
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for rem_xy in rem_holes:
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xy = xy[(xy != rem_xy).any(axis=1), ]
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return xy
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def l3_shift_perturbed_defect(
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mirror_dims: Sequence[int],
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perturbed_radius: float = 1.1,
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shifts_a: Sequence[float] = (),
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shifts_r: Sequence[float] = ()
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) -> NDArray[numpy.float64]:
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"""
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3-hole defect with perturbed hole sizes intended to form an upwards-directed
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beam. Can also include shifted holes along the defect line, intended
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to give the mode a more gaussian profile to improve Q.
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Args:
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mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
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is `2 * n + 1` in each direction.
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perturbed_radius: Amount to perturb the radius of the holes used for beam-forming
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shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line
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shifts_r: Factor to multiply the radius by. Should match length of `shifts_a`
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Returns:
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`[[x0, y0, r0], [x1, y1, r1], ...]` for all the holes
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"""
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xyr = ln_shift_defect(mirror_dims, 3, shifts_a, shifts_r)
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abs_x, abs_y = (numpy.fabs(xyr[:, i]) for i in (0, 1))
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# Sorted unique xs and ys
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# Ignore row y=0 because it might have shifted holes
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xs = numpy.unique(abs_x[abs_x != 0])
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ys = numpy.unique(abs_y)
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# which holes should be perturbed? (xs[[3, 7]], ys[1]) and (xs[[2, 6]], ys[2])
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perturbed_holes = numpy.array([(xs[a], ys[b]) for a, b in ((3, 1), (7, 1), (2, 2), (6, 2))])
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for row in xyr:
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if (numpy.fabs(row[:2])[None, :] == perturbed_holes).all(axis=1).any():
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row[2] = perturbed_radius
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return xyr
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