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(Probability_data, init):
descent = Gradient_Descent(setting,
Probability_data,
np.log(init),
stepsize=0.5,
alpha=0.2,
penalty=penalty)
stoprule = (rules.CombineRules(
(rules.CountIterations(500),
rules.RelativeChangeData(setting.Hcodomain.norm, Probability_data,
0))))
return descent.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)
gfu_noise = ngs.GridFunction(fes_codomain)
gfu_noise.Set(gfu_noise_order1)
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)
grid = UniformGrid(np.linspace(0, 2 * np.pi, 200))
op = Volterra(grid, exponent=3)
exact_solution = np.sin(grid.coords[0])
exact_data = op(exact_solution)
noise = 0.03 * op.domain.randn()
data = exact_data + noise
init = op.domain.ones()
setting = HilbertSpaceSetting(op=op, Hdomain=Sobolev, Hcodomain=L2)
landweber = Landweber(setting, data, init, stepsize=0.01)
stoprule = (
# Landweber is slow, so need to use large number of iterations
rules.CountIterations(max_iterations=100000) +
rules.Discrepancy(
setting.Hcodomain.norm, data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.1
)
)
reco, reco_data = landweber.run(stoprule)
plt.plot(grid.coords[0], exact_solution.T, label='exact solution')
plt.plot(grid.coords[0], reco, label='reco')
plt.plot(grid.coords[0], exact_data, label='exact data')
plt.plot(grid.coords[0], data, label='data')
plt.plot(grid.coords[0], reco_data, label='reco data')
plt.legend()
Hdomain=HilbertPullBack(Sobolev(index=2), embedding, inverse='cholesky'),
Hcodomain=L2
)
solver = IrgnmCG(
setting, data,
regpar=1, regpar_step=0.8,
init=init,
cgpars=dict(
tol=1e-8,
reltolx=1e-8,
reltoly=1e-8
)
)
stoprule = (
rules.CountIterations(100) +
rules.Discrepancy(
setting.Hcodomain.norm, data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.1
)
)
plt.ion()
fig, axes = plt.subplots(ncols=3, nrows=2, constrained_layout=True)
bars = np.vectorize(lambda ax: cbar.make_axes(ax)[0], otypes=[object])(axes)
axes[0, 0].set_title('exact contrast')
axes[1, 0].set_title('exact data')
axes[0, 1].set_title('reco contrast')
axes[1, 1].set_title('reco data')
data = op(exact_solution) + noise
plotmeshes(codomain, data=codomain.to_ngs(data))['data']
# ---
setting = HilbertSpaceSetting(op=op, Hdomain=L2, Hcodomain=L2)
reco, reco_data = IrgnmCG(
setting,
data,
init=domain.from_ngs(1 + ngs.x + 5 * ngs.x * (1 - ngs.x) * ngs.y *
(1 - ngs.y)),
regpar=0.1,
regpar_step=2 / 3,
cgstop=100,
).run(
rules.CountIterations(20) +
rules.Discrepancy(setting.Hcodomain.norm,
data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.01))
gfu_reco = op.domain.to_ngs(reco)
plots = plotmeshes(domain, reco=gfu_reco, error=cfu_exact_solution - gfu_reco)
plots['reco']
# ---
plots['error']
level=logging.INFO,
format='%(asctime)s %(levelname)s %(name)-20s :: %(message)s')
grid = UniformGrid(np.linspace(0, 2 * np.pi, 200))
op = Volterra(grid, exponent=3)
exact_solution = np.sin(grid.coords[0])
exact_data = op(exact_solution)
noise = 0.03 * op.domain.randn()
data = exact_data + noise
init = op.domain.ones()
setting = HilbertSpaceSetting(op=op, Hdomain=Sobolev(index=2), Hcodomain=L2)
solver = IrgnmCG(setting, data, regpar=1, regpar_step=0.9, init=init)
stoprule = (rules.CountIterations(max_iterations=100) +
rules.Discrepancy(setting.Hcodomain.norm,
data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.1))
reco, reco_data = solver.run(stoprule)
plt.plot(grid.coords[0], exact_solution.T, label='exact solution')
plt.plot(grid.coords[0], reco, label='reco')
plt.plot(grid.coords[0], exact_data, label='exact data')
plt.plot(grid.coords[0], data, label='data')
plt.plot(grid.coords[0], reco_data, label='reco data')
plt.legend()
plt.show()