def _update_boundary(self, x, y):
N = self.waveguide_params.get("N")
eta = self.waveguide_params.get("eta")
print "N:", N
print "eta: ", eta
k0, k1 = [ np.sqrt(N**2 - n**2)*np.pi for n in 0, 1 ]
L = abs(2*np.pi/(k0 - k1 + y))
if neumann:
WG = Neumann(L=L, loop_type='Constant', x_R0=x, y_R0=y,
**self.waveguide_params)
else:
WG = Dirichlet(L=L, loop_type='Constant', x_R0=x, y_R0=y,
**self.waveguide_params)
self.WG = WG
xi_lower, xi_upper = WG.get_boundary(eps=x, delta=y)
np.savetxt("lower.profile", zip(WG.t, xi_lower))
np.savetxt("upper.profile", zip(WG.t, xi_upper))
N_file = len(WG.t)
replacements = {'LENGTH': str(L),
'WIDTH': str(W),
'MODES': str(N),
'PPHW': str(self.pphw),
'GAMMA0': str(eta),
'NEUMANN': '0',
'N_FILE_BOUNDARY': str(N_file),
'BOUNDARY_UPPER': 'upper.boundary',
'BOUNDARY_LOWER': 'lower.boundary'}
replace_in_file(self.template, self.xml, **replacements)
def get_loop_eigenfunction(N=1.05, eta=0.0, L=5., d=1., eps=0.05, nx=None,
loop_direction="+", loop_type='Bell', init_state='a',
init_phase=0.0, mpi=False, pphw=100,
effective_model_only=False,
neumann=1):
"""Return the instantaneous eigenfunctions and eigenvectors for each step
in a parameter space loop.
Parameters:
-----------
N: float
Number of open modes (floor(N)).
eta: float
Dissipation strength.
L: float
System length.
d: float
System width.
eps: float
Half-maximum boundary roughness.
nx: int
Number of slices to calculate. If None, determine nx via
pphw and N automatically.
loop_direction: str
Loop direction of the parameter space trajectory. Allowed
values: + or -.
loop_type: str
Trajectory shape in parameter space.
init_state: str
Initial state of the evolution in the effective 2x2 system.
init_phase: float
Initial phase in the trajectory.
mpi: bool
Whether to use the parallel greens_code version.
pphw: int
Points per half-wavelength.
effective_model_only: bool
Whether to only calculate the effective model predictions.
neumann: int
Whether to use Neumann or Dirichlet boundary conditions.
"""
greens_path = os.environ.get('GREENS_CODE_XML')
XML = os.path.join(greens_path, "input_periodic_cell.xml")
wg_kwargs = {'N': N,
'eta': eta,
'L': L,
'init_phase': init_phase,
'init_state': init_state,
'loop_direction': loop_direction,
'loop_type': loop_type,
'x_R0': eps
}
if neumann:
WG = Neumann(**wg_kwargs)
else:
WG = DirichletReduced(**wg_kwargs)
_, b0, b1 = WG.solve_ODE()
# prepare waveguide and profile -------------------------------------------
profile_kwargs = {'eps': eps,
'pphw': pphw,
'input_xml': XML,
'custom_directory': os.getcwd(),
'neumann': neumann}
profile_kwargs.update(wg_kwargs)
ep.profile.Generate_Profiles(**profile_kwargs)
for file in glob.glob("N_*profile"):
if "lower" in file:
shutil.move(file, "boundary.lower_profile")
if "upper" in file:
shutil.move(file, "boundary.upper_profile")
# -------------------------------------------------------------------------
# trajectories ------------------------------------------------------------
if 0:
f, (ax1, ax2) = plt.subplots(nrows=2)
ax1.semilogy(WG.t, abs(b0), "r-")
ax1.semilogy(WG.t, abs(b1), "g-")
wg_kwargs['loop_direction'] = '+'
if neumann:
WG = Neumann(**wg_kwargs)
else:
WG = DirichletReduced(**wg_kwargs)
_, b0, b1 = WG.solve_ODE()
ax1.semilogy(WG.t, abs(b0[::-1]), "r--")
ax1.semilogy(WG.t, abs(b1[::-1]), "g--")
ax2.plot(WG.t, WG.eVals[:,0].real, "r-")
ax2.plot(WG.t, WG.eVals[:,1].real, "g-")
ax2.plot(WG.t, WG.eVals[:,0].imag, "r--")
ax2.plot(WG.t, WG.eVals[:,1].imag, "g--")
# plt.savefig("evals_trajectories.png")
plt.show()
# -------------------------------------------------------------------------
# change nx and ny accoring to pphw and modes -----------------------------
nyout = pphw*N
if nx is None:
nx = int(L*(nyout+1.))
print "nx:", nx
ny = int(d*(nyout+1.))
# -------------------------------------------------------------------------
x = np.linspace(0, L, nx)
y = np.linspace(0, d, ny)
eps, delta = WG.get_cycle_parameters(x)
K_0, K_1, Chi_0, Chi_1 = [ list() for n in range(4) ]
job_kwargs = {'eta': eta,
'pphw': pphw,
'XML': XML,
'N': N,
'WG': WG,
'loop_direction': loop_direction,
'neumann': neumann}
if not effective_model_only:
# serialized version:
results = []
for n, (xn, epsn, deltan) in enumerate(zip(x, eps, delta)):
run_single_job(n, xn, epsn, deltan, **job_kwargs)
# pool = multiprocessing.Pool(processes=multiprocessing.cpu_count())
# results = [ pool.apply_async(run_single_job, args=(n, xn, epsn, deltan),
# kwds=job_kwargs)
# for n, (xn, epsn, deltan) in enumerate(zip(x, eps, delta)) ]
# results = [ p.get() for p in results ]
# alternative parallelization:
# job_list = [ (n, xn, epsn, deltan, eta, pphw, XML, N, WG, loop_direction)
# for n, (xn, epsn, deltan) in enumerate(zip(x, eps, delta)) ]
# results = pool.map(run_single_job, job_list)
# properly unpack results
for res in results:
if res is None:
# reuse last set of eigenvalues/eigenvectors if something went
# wrong in the function call of run_single_job
print "Warning: calculation failed."
else:
K0, K1, ev0, ev1 = res
K_0.append(K0)
K_1.append(K1)
Chi_0.append(ev0)
Chi_1.append(ev1)
# -------------------------------------------------------------------------
# numerical data
K_0, K_1, Chi_0, Chi_1 = [ np.asarray(z) for z in K_0, K_1, Chi_0, Chi_1 ]
# smooth
K_0, K_1, Chi_0, Chi_1 = smooth_eigensystem(K_0, K_1, Chi_0, Chi_1,
eps=WG.x_R0, plot=False)
# transpose array!
Chi_0, Chi_1 = [ np.array(c).T for c in Chi_0, Chi_1 ]
# unwrapp phase
G = delta + WG.kr
L_range = 2*np.pi/G # make small error since L != r_nx*dx
K_0 = np.unwrap(K_0.real*L_range)/L_range + 1j*K_0.imag
K_1 = np.unwrap(K_1.real*L_range)/L_range + 1j*K_1.imag
# TODO: handle case for eps = 0.0
# remove discontinuous second order derivative (if we cross the DP)
# plt.plot(np.diff(np.abs(K_0), 2))
# plt.show()
# assemble eigenvectors
Chi_0 *= np.exp(1j*K_0*x)
Chi_1 *= np.exp(1j*K_1*x) * np.exp(-1j*WG.kr*x)
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# effective model predictons
# get eigensystem
Chi_0_eff, Chi_1_eff = WG.eVecs_r[:,:,0], WG.eVecs_r[:,:,1]
# Chi_0_eff, Chi_1_eff = b0, b1
K_0_eff, K_1_eff = WG.eVals[:,0], WG.eVals[:,1]
# interpolate
K_0_eff = (interp1d(WG.t, K_0_eff.real)(x) +
1j*interp1d(WG.t, K_0_eff.imag)(x))
K_1_eff = (interp1d(WG.t, K_1_eff.real)(x) +
1j*interp1d(WG.t, K_1_eff.imag)(x))
Chi_0_eff = [ (interp1d(WG.t, Chi_0_eff[:,n].real)(x) +
1j*interp1d(WG.t, Chi_0_eff[:,n].imag)(x)) for n in 0, 1 ]
Chi_1_eff = [ (interp1d(WG.t, Chi_1_eff[:,n].real)(x) +
1j*interp1d(WG.t, Chi_1_eff[:,n].imag)(x)) for n in 0, 1 ]
# Chi_0_eff = [ (interp1d(WG.t, Chi_0_eff[:].real)(x) +
# 1j*interp1d(WG.t, Chi_0_eff[:].imag)(x)) for n in 0, 1 ]
# Chi_1_eff = [ (interp1d(WG.t, Chi_1_eff[:].real)(x) +
# 1j*interp1d(WG.t, Chi_1_eff[:].imag)(x)) for n in 0, 1 ]
Chi_0_eff, Chi_1_eff = [ np.array(c).T for c in Chi_0_eff, Chi_1_eff ]
# fold back
G = delta + WG.kr
L_range = 2*np.pi/G # make small error since L != r_nx*dx
# np.savetxt("output_data.dat", zip(G, L_range, K_0_eff.real, K_1_eff.real,
# K_0.real, K_1.real),
# header='G L_range K_0_eff K_1_eff K_0 K_1')
K_0_eff = ((-K_0_eff.real + G/2.) % G - G/2.) + 1j*K_0_eff.imag
K_1_eff = ((-K_1_eff.real + G/2.) % G - G/2.) + 1j*K_1_eff.imag
# unwrapp phase
K_0_eff = np.unwrap(K_0_eff.real*L_range)/L_range + 1j*K_0_eff.imag
K_1_eff = np.unwrap(K_1_eff.real*L_range)/L_range + 1j*K_1_eff.imag
# assemble effective model eigenvectors
Chi_0_eff[:,0] *= np.exp(1j*K_0_eff*x)
Chi_0_eff[:,1] *= np.exp(1j*K_0_eff*x)
Chi_1_eff[:,0] *= np.exp(1j*K_1_eff*x)
Chi_1_eff[:,1] *= np.exp(1j*K_1_eff*x)
# no additional factor of np.exp(-i*kr*x) since we unwrap the phase,
# corresponding to K_n -> K_n + n*G
if neumann:
Chi_0_eff_0 = np.outer(Chi_0_eff[:,0], 1.*np.ones_like(y))
Chi_0_eff_1 = np.outer(Chi_0_eff[:,1], #*np.exp(-1j*WG.kr*x),
np.sqrt(2.*WG.k0/WG.k1)*np.cos(np.pi*y))
Chi_0_eff = Chi_0_eff_0 + Chi_0_eff_1
Chi_1_eff_0 = np.outer(Chi_1_eff[:,0], 1.*np.ones_like(y))
Chi_1_eff_1 = np.outer(Chi_1_eff[:,1], #*np.exp(-1j*WG.kr*x),
np.sqrt(2.*WG.k0/WG.k1)*np.cos(np.pi*y))
Chi_1_eff = Chi_1_eff_0 + Chi_1_eff_1
else:
Chi_0_eff_0 = np.outer(Chi_0_eff[:,0], np.sin(np.pi*y))
Chi_0_eff_1 = np.outer(Chi_0_eff[:,1], #*np.exp(-1j*WG.kr*x),
np.sqrt(WG.k1/WG.k0)*np.sin(2*np.pi*y))
Chi_0_eff = Chi_0_eff_0 + Chi_0_eff_1
Chi_1_eff_0 = np.outer(Chi_1_eff[:,0], np.sin(np.pi*y))
Chi_1_eff_1 = np.outer(Chi_1_eff[:,1], #*np.exp(-1j*WG.kr*x),
np.sqrt(WG.k1/WG.k0)*np.sin(2*np.pi*y))
Chi_1_eff = Chi_1_eff_0 + Chi_1_eff_1
Chi_0_eff, Chi_1_eff = [ c.T for c in Chi_0_eff, Chi_1_eff ]
# -------------------------------------------------------------------------
# eigenvalues -------------------------------------------------------------
if 1:
plt.clf()
f, (ax1, ax2, ax3) = plt.subplots(nrows=3, figsize=(8,6), dpi=80)
prop = {'size': 12}
if not effective_model_only:
ax1.set_title(r"Numerical eigenvalues $K_n$")
ax1.plot(x, K_0.real, "r-", label=r"$\Re{K_0}$")
ax1.plot(x, K_0.imag, "b-", label=r"$\Im{K_0}$")
ax1.plot(x, K_1.real, "r--", label=r"$\Re{K_1}$")
ax1.plot(x, K_1.imag, "b--", label=r"$\Im{K_1}$")
ax1.set_xlabel(r"$x$")
l1 = ax1.legend(bbox_to_anchor=(1.3,1.075), prop=prop)
ax2.set_title(r"Effective model eigenvalues $K^{\mathrm{eff}}_n$")
ax2.plot(x, K_0_eff.real, "r-", label=r"$\Re{K^{\mathrm{eff}}_0}$")
ax2.plot(x, K_0_eff.imag, "b-", label=r"$\Im{K^{\mathrm{eff}}_0}$")
ax2.plot(x, K_1_eff.real, "r--", label=r"$\Re{K^{\mathrm{eff}}_1}$")
ax2.plot(x, K_1_eff.imag, "b--", label=r"$\Im{K^{\mathrm{eff}}_1}$")
ax2.set_xlabel(r"$x$")
l2 = ax2.legend(bbox_to_anchor=(1.3,1.075), prop=prop)
extra_artist=[l2]
if not effective_model_only:
ax3.set_title("Comparison")
ax3.plot(x, abs(K_0 - K_0_eff)**2, "k-", label=r"$|K_0 - K^{\mathrm{eff}}_0|^2$")
ax3.plot(x, abs(K_1 - K_1_eff)**2, "k--", label=r"$|K_1 - K^{\mathrm{eff}}_1|^2$")
ax3.set_xlabel(r"$x$")
l3 = ax3.legend(bbox_to_anchor=(1.3,1.075), prop=prop)
extra_artist=[l3]
plt.tight_layout()
plt.savefig("eigenvalues.png", bbox_extra_artists=(extra_artist),
bbox_inches='tight')
# ------------------------------------------------------------------------
# save potential ----------------------------------------------------------
# for n, c in enumerate((Chi_0, Chi_1)):
# c = np.abs(c).flatten(order='F')
# nfile = range(len(c))
# np.savetxt("potential_imag_{}.dat".format(n),
# zip(nfile, c), fmt='%i %10.6f')
# c = (c.max() - c)/c.max()
# np.savetxt("potential_imag_{}_normalized.dat".format(n),
# zip(nfile, c), fmt='%i %10.6f')
wavefunctions = [Chi_0_eff, Chi_1_eff]
names = ["Chi_0_eff", "Chi_1_eff"]
if not effective_model_only:
wavefunctions += [Chi_0, Chi_1]
names += ["Chi_0", "Chi_1"]
for n, c in zip(names, wavefunctions):
np.savetxt("potential_{}.dat".format(n), c)
c = np.abs(c).flatten(order='F')
nfile = range(len(c))
np.savetxt("potential_{}_imag.dat".format(n),
zip(nfile, c), fmt='%i %10.6f')
c = (c.max() - c)/c.max()
np.savetxt("potential_{}_imag_normalized.dat".format(n),
zip(nfile, c), fmt='%i %10.6f')
# -------------------------------------------------------------------------
X, Y = np.meshgrid(x, y)
for part in np.abs, np.angle, np.real, np.imag:
if part == np.abs:
cmap = 'Reds'
else:
cmap = 'RdBu_r'
if not effective_model_only:
plt.clf()
Z = part(Chi_0)
p = plt.pcolormesh(X, Y, Z, cmap=cmap)
plt.colorbar(p)
plt.savefig("Chi_0_{0.__name__}.png".format(part))
plt.clf()
Z = part(Chi_1)
p = plt.pcolormesh(X, Y, Z, cmap=cmap)
plt.colorbar(p)
plt.savefig("Chi_1_{0.__name__}.png".format(part))
plt.clf()
Z_eff = part(Chi_0_eff)
p = plt.pcolormesh(X, Y[::-1,:], Z_eff, cmap=cmap)
plt.colorbar(p)
plt.savefig("Chi_0_eff_{0.__name__}.png".format(part))
plt.clf()
Z_eff = part(-1j*Chi_1_eff)
p = plt.pcolormesh(X, Y[::-1,:], Z_eff, cmap=cmap)
plt.colorbar(p)
plt.savefig("Chi_1_eff_{0.__name__}.png".format(part))