def test_eigenwave(self):
w = wave.eigenwave((4, 3), 0, 0, amplitude=4 * 3)
self.allclose(w, np.ones((4, 3)))
w = wave.eigenwave((4, 3), 0, 0)
self.allclose(w, np.ones((4, 3)))
out = np.empty_like(w)
wave.eigenwave((4, 3), 0, 0, out=out)
self.allclose(out, np.ones((4, 3)))
self.iscomplex(out)
def test_wave2eigenwave(self):
w = wave.planewave((12, 14), (1, 2), 0.5, 0)
e = wave.wave2eigenwave(w)
e0 = wave.eigenwave((12, 14), 0, 1)
self.allclose(e[0], e0)
e0 = wave.eigenwave((12, 14), 0, 2)
self.allclose(e[1], e0)
out = np.empty_like(e)
wave.wave2eigenwave(w, out=out)
self.allclose(out, e)
self.iscomplex(e)
def propagate_4x4_full(field,
wavenumbers,
layer,
nsteps=1,
betamax=BETAMAX,
out=None):
shape = field.shape[-2:]
d, epsv, epsa = layer
kd = wavenumbers * d / nsteps
if out is None:
out = np.empty_like(field)
out_af = None
pm = None
ii, jj = np.meshgrid(range(shape[0]),
range(shape[1]),
copy=False,
indexing="ij")
for step in range(nsteps):
for i in range(len(wavenumbers)):
ffield = fft2(field[..., i, :, :, :])
ofield = np.zeros_like(out[..., i, :, :, :])
b, p = betaphi(shape, wavenumbers[i])
mask = b < betamax
amplitude = ffield[..., mask]
betas = b[mask]
phis = p[mask]
iind = ii[mask]
jind = jj[mask]
for bp in sorted(zip(range(len(betas)), betas, phis, iind, jind),
key=lambda el: el[1],
reverse=False):
#for j,bp in enumerate(zip(betas,phis,iind,jind)):
j, beta, phi, ieig, jeig = bp
out_af = alphaffi(beta, phi, epsv, epsa, out=out_af)
alpha, f, fi = out_af
pm = phasem(alpha, kd[i], out=pm)
w = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=amplitude[..., j])
w = dotmdmf(f, pm, fi, w, out=w)
np.add(ofield, w, ofield)
out[..., i, :, :, :] = ofield
field = out
return out
def test_planewave_k(self):
shape = (13, 11)
for k in (0.1, 1., 10):
b, p = wave.betaphi(shape, k)
for i in range(shape[0]):
for j in range(shape[1]):
w1 = wave.planewave(shape, k, b[i, j], p[i, j])
w2 = wave.eigenwave(shape, i, j)
self.allclose(w1, w2)
def test_planewave_shapes(self):
shapes = ((16, 16), (15, 15), (12, 13), (7, 6))
k = 1
for shape in shapes:
b, p = wave.betaphi(shape, k)
for i in range(shape[0]):
for j in range(shape[1]):
w1 = wave.planewave(shape, k, b[i, j], p[i, j])
w2 = wave.eigenwave(shape, i, j)
self.allclose(w1, w2)
def _layer_mat3d(k0, d, epsv, epsa, mask, betas, phis, indices, method):
n = len(betas)
kd = k0 * d #/2.
shape = epsv.shape[-3], epsv.shape[-2]
if method.startswith("2x2"):
out = np.empty(shape=(n, n, 2, 2), dtype=CDTYPE)
else:
out = np.empty(shape=(n, n, 4, 4), dtype=CDTYPE)
for j, (beta, phi) in enumerate(zip(betas, phis)):
if method.startswith("2x2"):
alpha, fmat = alphaf(beta, phi, epsv, epsa)
f = tmm.E_mat(fmat, mode=+1, copy=False)
fi = inv(f)
pmat = phase_mat(alpha[..., ::2], kd)
else:
alpha, f, fi = alphaffi(beta, phi, epsv, epsa)
pmat = phase_mat(alpha, -kd)
if method == "4x4_1":
pmat[..., 1::2] = 0.
if method != "4x4":
raise ValueError("Unsupported method.")
wave = eigenwave(shape, indices[j, 0], indices[j, 1], amplitude=1.)
m = dotmdm(f, pmat, fi)
mw = m * wave[..., None, None]
mf = mfft2(mw, overwrite_x=True)
#dd = np.linspace(0,1.,10)*d
# dmat = 0.
# for dm in dd:
# dmat = dmat + second_field_diffraction_matrix(shape, -k0, beta, phi,dm,
# epsv = (1.5,1.5,1.5),
# epsa = (0.,0.,0.), betamax = 1.4) /len(dd)
# mf = dotmm(dmat,mf)
mf = mf[mask, ...]
out[:, j, :, :] = mf
return out
def propagate_2x2_full(field,
wavenumbers,
layer,
input_layer=None,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None):
shape = field.shape[-2:]
d, epsv, epsa = layer
if input_layer is not None:
d_in, epsv_in, epsa_in = input_layer
kd = wavenumbers * d / nsteps
if out is None:
out = np.empty_like(field)
ii, jj = np.meshgrid(range(shape[0]),
range(shape[1]),
copy=False,
indexing="ij")
for step in range(nsteps):
for i in range(len(wavenumbers)):
ffield = fft2(field[..., i, :, :, :])
ofield = np.zeros_like(out[..., i, :, :, :])
b, p = betaphi(shape, wavenumbers[i])
mask = b < betamax
amplitude = ffield[..., mask]
betas = b[mask]
phis = p[mask]
iind = ii[mask]
jind = jj[mask]
if bulk is not None:
obulk = bulk[..., i, :, :, :]
if refl is not None:
tampl = fft2(refl[..., i, :, :, :])[..., mask]
orefl = refl[..., i, :, :, :]
orefl[...] = 0.
for bp in sorted(zip(range(len(betas)), betas, phis, iind, jind),
key=lambda el: el[1],
reverse=False):
#for j,bp in enumerate(zip(betas,phis,iind,jind)):
j, beta, phi, ieig, jeig = bp
out_af = alphaf(beta, phi, epsv, epsa)
alpha, fmat_out = out_af
e = E_mat(fmat_out, mode=mode)
ei0 = inv(e)
ei = ei0
pm = phase_mat(alpha, kd[i, None, None], mode=mode)
w = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=amplitude[..., j])
if step == 0 and reflection != False:
alphain, fmat_in = alphaf(beta, phi, epsv_in, epsa_in)
if refl is not None:
ei, eri = Etri_mat(fmat_in, fmat_out, mode=mode)
ein = E_mat(fmat_in, mode=-1 * mode)
t = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=tampl[..., j])
r = dotmf(eri, w)
r = dotmf(ein, r, out=r)
np.add(orefl, r, orefl)
w = dotmf(ei, w, out=w)
t = dotmf(ei0, t, out=t)
w = np.add(t, w, out=w)
else:
ei = Eti_mat(fmat_in, fmat_out, mode=mode)
w = dotmf(ei, w, out=w)
w = dotmf(dotmd(e, pm), w, out=w)
np.add(ofield, w, ofield)
else:
w = dotmdmf(e, pm, ei, w, out=w)
np.add(ofield, w, ofield)
if bulk is not None:
e2h = E2H_mat(fmat_out, mode=mode)
obulk[..., 1::2, :, :] += dotmf(e2h, w)
obulk[..., ::2, :, :] += w
out[..., i, :, :, :] = ofield
field = out
return out, refl
def test_eigenwave1(self):
w = wave.eigenwave((1, 12), 0, 2)
w1 = wave.eigenwave1(12, 2)
self.allclose(w[0, :], w1)
w1 = wave.eigenwave1(12, 2, amplitude=12)
self.allclose(w[0, :], w1)