def perform_inversion(data, init, sigma, vel):
op = LymanAlphaHydrogen(domain,
parameters_inversion,
redshift,
redshift,
hubble,
hubble,
vel_pec=vel,
codomain=codomain)
setting = HilbertSpaceSetting(op=op, Hdomain=L2, Hcodomain=L2)
richardson = RLHydrogen(op)
richardson_lucy = Richardson_Lucy(setting, data, init, richardson, m=3)
energy = EnergyNorm(sigma)
stoprule = (rules.CombineRules(
(rules.CountIterations(300),
rules.Discrepancy(energy.norm,
data,
noiselevel=np.sqrt(N_spect),
tau=1),
rules.RelativeChangeData(energy.norm, data, 0.0001))))
return richardson_lucy.run(stoprule)
def perform_inversion(data, init, sigma, vel):
C_D = sigma
op = LymanAlphaBar(domain,
parameters_inversion,
redshift,
redshift,
hubble,
hubble,
vel,
gamma=True,
codomain=codomain)
setting = HilbertSpaceSetting(op=op, Hdomain=L2, Hcodomain=L2)
solver = IRGN(setting,
data,
init,
C_0,
M_0,
C_D**2,
maxit=15,
tol=1e-3,
restart=10)
energy = EnergyNorm(sigma)
stoprule = (rules.CombineRules(
(rules.CountIterations(10),
rules.Discrepancy(energy.norm,
data,
noiselevel=np.sqrt(N_spect),
tau=1),
rules.RelativeChangeData(energy.norm, data, 0.1))))
return solver.run(stoprule)
noise = gfu_noise.vec.FV().NumPy()
data = exact_data + noise
init = 1 + ngs.x**2
init_gfu = ngs.GridFunction(op.fes_domain)
init_gfu.Set(init)
init_solution = init_gfu.vec.FV().NumPy().copy()
init_data = op(init_solution)
setting = HilbertSpaceSetting(op=op, Hdomain=L2, Hcodomain=Sobolev)
landweber = Landweber(setting, data, init_solution, stepsize=1)
stoprule = (rules.CountIterations(1000) +
rules.Discrepancy(setting.Hcodomain.norm,
data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.1))
reco, reco_data = landweber.run(stoprule)
ngs.Draw(exact_solution_coeff, op.fes_domain.mesh, "exact")
ngs.Draw(init, op.fes_domain.mesh, "init")
# Draw recondtructed solution
gfu_reco = ngs.GridFunction(op.fes_domain)
gfu_reco.vec.FV().NumPy()[:] = reco
coeff_reco = ngs.CoefficientFunction(gfu_reco)
ngs.Draw(coeff_reco, op.fes_domain.mesh, "reco")
# Draw data space
init = smoothed_op.domain.zeros()
init_density, _ = smoothed_op.domain.split(init)
init_density[...] = 1
setting = HilbertSpaceSetting(op=smoothed_op, Hdomain=L2, Hcodomain=L2)
solver = IrgnmCG(setting=setting,
data=data,
regpar=10,
regpar_step=0.8,
init=init)
stoprule = (
rules.CountIterations(max_iterations=100) +
rules.Discrepancy(setting.Hcodomain.norm,
data,
noiselevel=setting.Hcodomain.norm(exact_data - data),
tau=1.1))
# Plotting setup
plt.ion()
fig, axes = plt.subplots(ncols=2, constrained_layout=True)
bars = [cbar.make_axes(ax)[0] for ax in axes]
axes[0].set_title('exact solution')
axes[1].set_title('reconstruction')
# Plot exact solution
im = axes[0].imshow(normalize(*mri_op.domain.split(exact_solution)))
fig.colorbar(im, cax=bars[0])
# Run the solver, plot iterates