def get_weights_circ(r, Nbar, Y):
"""
it evaluates integral weights,
which are used for upper-lower bounds calculation,
with constant circular inclusion
Parameters
----------
r - the parameter determining the size of inclusion
Nbar - no. of points of regular grid where the weights are evaluated
Y - the size of periodic unit cell
Returns
-------
Wphi - integral weights at regular grid sizing Nbar
"""
d = np.size(Y)
ZN2l = Grid.get_ZNl(Nbar)
meas_puc = np.prod(Y)
circ = 0
for m in np.arange(d):
Nshape = np.ones(d)
Nshape[m] = Nbar[m]
Nrep = np.copy(Nbar)
Nrep[m] = 1
xi_p2 = np.tile(np.reshape((ZN2l[m]/Y[m])**2, Nshape), Nrep)
circ += xi_p2
circ = circ**0.5
ind = tuple(np.round(Nbar/2))
circ[ind] = 1.
Wphi = r**2 * sp.jn(1, 2*np.pi*circ*r) / (circ*r)
Wphi[ind] = np.pi*r**2
Wphi = Wphi / meas_puc
return Wphi
def get_weights_circ(r, Nbar, Y):
"""
it evaluates integral weights,
which are used for upper-lower bounds calculation,
with constant circular inclusion
Parameters
----------
r - the parameter determining the size of inclusion
Nbar - no. of points of regular grid where the weights are evaluated
Y - the size of periodic unit cell
Returns
-------
Wphi - integral weights at regular grid sizing Nbar
"""
d = np.size(Y)
ZN2l = Grid.get_ZNl(Nbar)
meas_puc = np.prod(Y)
circ = 0
for m in np.arange(d):
Nshape = np.ones(d)
Nshape[m] = Nbar[m]
Nrep = np.copy(Nbar)
Nrep[m] = 1
xi_p2 = np.tile(np.reshape((ZN2l[m] / Y[m])**2, Nshape), Nrep)
circ += xi_p2
circ = circ**0.5
ind = tuple(np.round(Nbar / 2))
circ[ind] = 1.
Wphi = r**2 * sp.jn(1, 2 * np.pi * circ * r) / (circ * r)
Wphi[ind] = np.pi * r**2
Wphi = Wphi / meas_puc
return Wphi
def get_shift_inclusion(N, h, Y):
N = np.array(N, dtype=np.int32)
Y = np.array(Y, dtype=np.float64)
dim = N.size
ZN = Grid.get_ZNl(N)
SS = np.ones(N, dtype=np.complex128)
for ii in np.arange(dim):
Nshape = np.ones(dim)
Nshape[ii] = N[ii]
Nrep = N
Nrep[ii] = 1
SS *= np.tile(np.reshape(np.exp(-2*np.pi*1j*(h[ii]*ZN[ii]/Y[ii])),
Nshape), Nrep)
return SS
def get_shift_inclusion(N, h, Y):
N = np.array(N, dtype=np.int32)
Y = np.array(Y, dtype=np.float64)
dim = N.size
ZN = Grid.get_ZNl(N)
SS = np.ones(N, dtype=np.complex128)
for ii in np.arange(dim):
Nshape = np.ones(dim)
Nshape[ii] = N[ii]
Nrep = N
Nrep[ii] = 1
SS *= np.tile(
np.reshape(np.exp(-2 * np.pi * 1j * (h[ii] * ZN[ii] / Y[ii])),
Nshape), Nrep)
return SS
def matrix(self):
"""
This function returns the object as a matrix of DFT or iDFT resp.
"""
prodN = np.prod(self.N)
proddN = self.d*prodN
DTM = np.zeros(np.hstack([self.N, self.N]), dtype=np.complex128)
ZNl = Grid.get_ZNl(self.N)
if not self.inverse:
coef = 1./np.prod(self.N)
else:
coef = np.prod(self.N)
for nx in ZNl[0]:
for ny in ZNl[1]:
IM = np.zeros(np.array(self.N), dtype=np.float64)
IM[nx, ny] = 1
DTM[nx, ny, :, :] = coef*DFT.fftnc(IM, self.N)
import numpy.matlib as npmatlib
DTMd = npmatlib.zeros([proddN, proddN], dtype=np.complex128)
for ii in np.arange(self.d):
DTMd[prodN*ii:prodN**(ii+1), prodN*ii:prodN**(ii+1)] = DTM
return DTMd