def test_gaussian_energy(space, nonlinearity, noise, seed):
np.random.seed(seed)
dim = len(space.shape)
hspace = space.get_default_codomain()
ht = ift.HarmonicTransformOperator(hspace, target=space)
binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
pspace = ift.PowerSpace(hspace, binbounds=binbounds)
Dist = ift.PowerDistributor(target=hspace, power_space=pspace)
xi0 = ift.Field.from_random(domain=hspace, random_type='normal')
def pspec(k):
return 1 / (1 + k**2)**dim
pspec = ift.PS_field(pspace, pspec)
A = Dist(ift.sqrt(pspec))
N = ift.ScalingOperator(noise, space)
n = N.draw_sample()
R = ift.ScalingOperator(10., space)
def d_model():
if nonlinearity == "":
return R(ht(ift.makeOp(A)))
else:
tmp = ht(ift.makeOp(A))
nonlin = getattr(tmp, nonlinearity)()
return R(nonlin)
d = d_model()(xi0) + n
if noise == 1:
N = None
energy = ift.GaussianEnergy(d, N)(d_model())
ift.extra.check_jacobian_consistency(energy, xi0, ntries=10, tol=5e-8)
def test_hamiltonian_and_KL(field):
field = field.exp()
space = field.domain
lh = ift.GaussianEnergy(domain=space)
hamiltonian = ift.StandardHamiltonian(lh)
ift.extra.check_jacobian_consistency(hamiltonian, field)
S = ift.ScalingOperator(1., space)
samps = [S.draw_sample() for i in range(3)]
kl = ift.AveragedEnergy(hamiltonian, samps)
ift.extra.check_jacobian_consistency(kl, field)
### SETTING UP SPECIFIC SCENARIO ####
R = ift.GeometryRemover(position_space)
data_space = R.target
signal_response = R(correlated_field)
# Set up likelihood and load data
N = ift.ScalingOperator(0.1, data_space)
data, ground_truth = generate_mysterious_data(position_space)
data = ift.from_global_data(data_space, data)
likelihood = ift.GaussianEnergy(mean=data,
inverse_covariance=N.inverse)(signal_response)
#### SOLVING PROBLEM ####
ic_sampling = ift.GradientNormController(iteration_limit=100)
ic_newton = ift.GradInfNormController(
name='Newton', tol=1e-6, iteration_limit=30)
minimizer = ift.NewtonCG(ic_newton)
H = ift.StandardHamiltonian(likelihood, ic_sampling)
initial_mean = ift.MultiField.full(H.domain, 0.)
mean = initial_mean
# number of samples used to estimate the KL
N_samples = 10
def test_gaussian(field):
energy = ift.GaussianEnergy(domain=field.domain)
ift.extra.check_jacobian_consistency(energy, field)
data_space = R.target
noise = .001
N = ift.ScalingOperator(noise, data_space)
# Generate mock signal and data
mock_position = ift.from_random('normal', signal_response.domain)
data = signal_response(mock_position) + N.draw_sample()
# Minimization parameters
ic_sampling = ift.GradientNormController(iteration_limit=100)
ic_newton = ift.GradInfNormController(
name='Newton', tol=1e-7, iteration_limit=35)
minimizer = ift.NewtonCG(ic_newton)
# Set up likelihood and information Hamiltonian
likelihood = ift.GaussianEnergy(mean=data, covariance=N)(signal_response)
H = ift.StandardHamiltonian(likelihood, ic_sampling)
initial_mean = ift.MultiField.full(H.domain, 0.)
mean = initial_mean
plot = ift.Plot()
plot.add(signal(mock_position), title='Ground Truth')
plot.add(R.adjoint_times(data), title='Data')
plot.add([A.force(mock_position)], title='Power Spectrum')
plot.output(ny=1, nx=3, xsize=24, ysize=6, name=filename.format("setup"))
# number of samples used to estimate the KL
N_samples = 20
# Draw new samples to approximate the KL five times