import nifty5 as ift from nifty5.library.los_response import LOSResponse from nifty5.library.amplitude_model import make_amplitude_model from nifty5.library.smooth_sky import make_correlated_field import numpy as np from scipy.io import loadmat def get_random_LOS(n_los): starts = list(np.random.uniform(0, 1, (n_los, 2)).T) ends = list(np.random.uniform(0, 1, (n_los, 2)).T) return starts, ends if __name__ == '__main__': # ## ABOUT THIS TUTORIAL np.random.seed(42) position_space = ift.RGSpace([128, 128]) # Setting up an amplitude model A, amplitude_internals = make_amplitude_model( position_space, 16, 1, 10, -4., 1, 0., 1.) # Building the model for a correlated signal harmonic_space = position_space.get_default_codomain() ht = ift.HarmonicTransformOperator(harmonic_space, position_space) power_space = A.value.domain[0] power_distributor = ift.PowerDistributor(harmonic_space, power_space) position = {} position['xi'] = ift.Field.from_random('normal', harmonic_space) position = ift.MultiField(position) xi = ift.Variable(position)['xi'] Amp = power_distributor(A) correlated_field_h = Amp * xi correlated_field = ht(correlated_field_h) # # alternatively to the block above one can do: # correlated_field, _ = make_correlated_field(position_space, A) # apply some nonlinearity signal = ift.PointwisePositiveTanh(correlated_field) # Building the Line of Sight response LOS_starts, LOS_ends = get_random_LOS(100) R = LOSResponse(position_space, starts=LOS_starts, ends=LOS_ends) # build signal response model and model likelihood signal_response = R(signal) # specify noise data_space = R.target noise = .001 N = ift.ScalingOperator(noise, data_space) # generate mock data MOCK_POSITION = ift.from_random('normal', signal.position.domain) data = signal_response.at(MOCK_POSITION).value + N.draw_sample() # set up model likelihood likelihood = ift.GaussianEnergy(signal_response, mean=data, covariance=N) # set up minimization and inversion schemes ic_cg = ift.GradientNormController(iteration_limit=10) ic_sampling = ift.GradientNormController(iteration_limit=100) ic_newton = ift.GradientNormController(name='Newton', iteration_limit=100) minimizer = ift.RelaxedNewton(ic_newton) # build model Hamiltonian H = ift.Hamiltonian(likelihood, ic_cg, iteration_controller_sampling=ic_sampling) INITIAL_POSITION = ift.from_random('normal', H.position.domain) position = INITIAL_POSITION ift.plot(signal.at(MOCK_POSITION).value, name='truth.pdf') ift.plot(R.adjoint_times(data), name='data.pdf') ift.plot([A.at(MOCK_POSITION).value], name='power.pdf') # number of samples used to estimate the KL N_samples = 20 for i in range(5): H = H.at(position) samples = [H.curvature.draw_sample(from_inverse=True) for _ in range(N_samples)] KL = ift.SampledKullbachLeiblerDivergence(H, samples) KL = KL.makeInvertible(ic_cg) KL, convergence = minimizer(KL) position = KL.position ift.plot(signal.at(position).value, name='reconstruction.pdf') ift.plot([A.at(position).value, A.at(MOCK_POSITION).value], name='power.pdf') avrg = 0. va = 0. powers = [] for sample in samples: sam = signal.at(sample + position).value powers.append(A.at(sample+position).value) avrg += sam va += sam**2 avrg /= len(samples) va /= len(samples) va -= avrg**2 std = ift.sqrt(va) ift.plot(avrg, name='avrg.pdf') ift.plot(std, name='std.pdf') ift.plot([A.at(position).value, A.at(MOCK_POSITION).value]+powers, name='power.pdf')