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import meep as mp
import numpy as np
from scipy import sparse
#from autograd import grad, jacobian, vector_jacobian_product
import autograd.numpy as npa
from autograd import grad, jacobian
#invoke python's 'abstract base class' formalism in a version-agnostic way
from abc import ABCMeta, abstractmethod
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 if volume else 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(BilinearInterpolationBasis, self).__init__(**kwargs)
# Generate interpolation grid
if symmetry is None or len(symmetry) == 0:
self.symmetry = []
else:
self.symmetry = symmetry
if mp.X in set(self.symmetry):
self.Nx = int(resolution * self.volume.size.x / 2)
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)
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)
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)
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
# From matrix vectors, populate the sparse matrix
A = sparse.coo_matrix((interp_weights, (row_ind, col_ind)),shape=(output_dimension, input_dimension))
return A
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