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from abc import ABCMeta, abstractmethod
import numpy as np
from scipy import sparse
import meep as mp
ABC = ABCMeta("ABC", (object,), {"__slots__": ()}) # compatible with Python 2 and 3
# ----------------------------------------------------------------------
# Basis is the abstract base class from which classes describing specific
# basis sets should inherit.
# ----------------------------------------------------------------------
class Basis(ABC):
""" """
def __init__(
self,
rho_vector=None,
volume=None,
size=None,
center=mp.Vector3(),
):
self.volume = volume or mp.Volume(center=center, size=size)
self.rho_vector = rho_vector
def func(self):
def _f(p):
return self(p)
return _f
@abstractmethod
def get_basis_vjp(self):
raise NotImplementedError("derived class must implement get_basis_vjp method")
@abstractmethod
def __call__(self, p=[0.0, 0.0]):
raise NotImplementedError("derived class must implement __call__() method")
def set_rho_vector(self, rho_vector):
self.rho_vector = rho_vector
# -------------------------------- #
# Bilinear Interpolation Basis class
# -------------------------------- #
class BilinearInterpolationBasis(Basis):
"""
Simple bilinear interpolation basis set.
"""
def __init__(self, resolution, symmetry=None, **kwargs):
self.dim = 2
super().__init__(**kwargs)
# Generate interpolation grid
self.symmetry = [] if symmetry is None or len(symmetry) == 0 else symmetry
if mp.X in set(self.symmetry):
self.Nx = int(resolution * self.volume.size.x / 2) + 1
self.rho_x = np.linspace(
self.volume.center.x,
self.volume.center.x + self.volume.size.x / 2,
self.Nx,
)
self.mirror_X = True
else:
self.Nx = int(resolution * self.volume.size.x) + 1
self.rho_x = np.linspace(
self.volume.center.x - self.volume.size.x / 2,
self.volume.center.x + self.volume.size.x / 2,
self.Nx,
)
self.mirror_X = False
if mp.Y in set(self.symmetry):
self.Ny = int(resolution * self.volume.size.y / 2) + 1
self.rho_y = np.linspace(
self.volume.center.y,
self.volume.center.y + self.volume.size.y / 2,
self.Ny,
)
self.mirror_Y = True
else:
self.Ny = int(resolution * self.volume.size.y) + 1
self.rho_y = np.linspace(
self.volume.center.y - self.volume.size.y / 2,
self.volume.center.y + self.volume.size.y / 2,
self.Ny,
)
self.mirror_Y = False
self.num_design_params = self.Nx * self.Ny
if self.rho_vector is None:
self.rho_vector = np.ones((self.num_design_params,))
def __call__(self, p):
x = (
2 * self.volume.center.x - p.x
if self.mirror_X and p.x < self.volume.center.x
else p.x
)
y = (
2 * self.volume.center.y - p.y
if self.mirror_Y and p.y < self.volume.center.y
else p.y
)
weights, interp_idx = self.get_bilinear_row(
x, y, self.rho_x, self.rho_y
) # ignore z coordinate
return np.dot(self.rho_vector[interp_idx], weights)
def get_basis_vjp(self, dJ_deps, design_grid):
"""get vector jacobian product of interpolator"""
dg_Nx, dg_Ny, Nz, Nf = dJ_deps.shape # get important design grid dimensions
x_grid = design_grid.x
y_grid = design_grid.y
z_grid = design_grid.z
# take care of symmetries
if self.mirror_X:
dJ_deps = dJ_deps[int(dg_Nx / 2) :, :, :, :] * 2
x_grid = x_grid[int(dg_Nx / 2) :]
if self.mirror_Y:
dJ_deps = dJ_deps[:, int(dg_Ny / 2) :, :, :] * 2
y_grid = y_grid[int(dg_Ny / 2) :]
dg_Nx, dg_Ny, Nz, Nf = dJ_deps.shape # recalculate
Nx, Ny = (
self.rho_x.size,
self.rho_y.size,
) # get important interpolator dimensions
# same interpolation matrix for all frequencies and all coordinates in Z direction
A = self.gen_interpolation_matrix(
self.rho_x, self.rho_y, x_grid, y_grid, z_grid
)
# TODO ditch the for loops
dJ_dp = np.zeros((Nx * Ny, Nf))
for fi in range(Nf):
for zi in range(Nz):
dJ_dp[:, fi] += np.matmul(
dJ_deps[:, :, zi, fi].reshape(dg_Nx * dg_Ny, order="C"), A
)
return dJ_dp
def get_bilinear_coefficients(self, x, x1, x2, y, y1, y2):
"""
Calculates the bilinear interpolation coefficients for a single point at (x,y).
Assumes that the user already knows the four closest points and provides the corresponding
(x1,x2) and(y1,y2) coordinates.
"""
b11 = ((x - x2) * (y - y2)) / ((x1 - x2) * (y1 - y2))
b12 = -((x - x2) * (y - y1)) / ((x1 - x2) * (y1 - y2))
b21 = -((x - x1) * (y - y2)) / ((x1 - x2) * (y1 - y2))
b22 = ((x - x1) * (y - y1)) / ((x1 - x2) * (y1 - y2))
return [b11, b12, b21, b22]
def get_bilinear_row(self, rx, ry, rho_x, rho_y):
"""
Calculates a vector of bilinear interpolation weights that can be used
in an inner product with the neighboring function values, or placed
inside of an interpolation matrix.
"""
Nx = rho_x.size
Ny = rho_y.size
# binary search in x direction to get x1 and x2
xi2 = np.searchsorted(rho_x, rx, side="left")
if xi2 <= 0: # extrapolation (be careful!)
xi1 = 0
xi2 = 1
elif xi2 >= Nx - 1: # extrapolation (be careful!)
xi1 = Nx - 2
xi2 = Nx - 1
else:
xi1 = xi2 - 1
x1 = rho_x[xi1]
x2 = rho_x[xi2]
# binary search in y direction to get y1 and y2
yi2 = np.searchsorted(rho_y, ry, side="left")
if yi2 <= 0: # extrapolation (be careful!)
yi1 = 0
yi2 = 1
elif yi2 >= Ny - 1: # extrapolation (be careful!)
yi1 = Ny - 2
yi2 = Ny - 1
else:
yi1 = yi2 - 1
y1 = rho_y[yi1]
y2 = rho_y[yi2]
# get weights
weights = self.get_bilinear_coefficients(rx, x1, x2, ry, y1, y2)
# get location of nearest neigbor interpolation points
interp_idx = np.array(
[xi1 * Ny + yi1, xi1 * Ny + yi2, (xi2) * Ny + yi1, (xi2) * Ny + yi2],
dtype=np.int64,
)
return weights, interp_idx
def gen_interpolation_matrix(
self,
rho_x,
rho_y,
rho_x_interp,
rho_y_interp,
rho_z_interp,
):
"""
Generates a bilinear interpolation matrix.
Arguments:
rho_x ................ [N,] numpy array - original x array mapping to povided data
rho_y ................ [N,] numpy array - original y array mapping to povided data
rho_x_interp ......... [N,] numpy array - new x array mapping to desired interpolated data
rho_y_interp ......... [N,] numpy array - new y array mapping to desired interpolated data
Returns:
A .................... [N,M] sparse matrix - interpolation matrix
"""
Nx = rho_x.size
Ny = rho_y.size
Nx_interp = np.array(rho_x_interp).size
Ny_interp = np.array(rho_y_interp).size
Nz_interp = np.array(rho_y_interp).size
input_dimension = Nx * Ny
output_dimension = Nx_interp * Ny_interp
interp_weights = np.zeros(4 * output_dimension)
row_ind = np.zeros(4 * output_dimension, dtype=np.int64)
col_ind = np.zeros(4 * output_dimension, dtype=np.int64)
ri = 0
for rx in rho_x_interp:
for ry in rho_y_interp:
# get weights
weights, interp_idx = self.get_bilinear_row(rx, ry, rho_x, rho_y)
# populate sparse matrix vectors
interp_weights[4 * ri : 4 * (ri + 1)] = weights
row_ind[4 * ri : 4 * (ri + 1)] = np.array(
[ri, ri, ri, ri], dtype=np.int64
)
col_ind[4 * ri : 4 * (ri + 1)] = interp_idx
ri += 1
return sparse.coo_matrix(
(interp_weights, (row_ind, col_ind)),
shape=(output_dimension, input_dimension),
)
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