# This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # # Copyright(C) 2013-2018 Max-Planck-Society # # NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik # and financially supported by the Studienstiftung des deutschen Volkes. import nifty5 as ift import numpy as np if __name__ == '__main__': # FIXME ABOUT THIS CODE np.random.seed(41) # Set up the position space of the signal # # # One dimensional regular grid with uniform exposure # position_space = ift.RGSpace(1024) # exposure = np.ones(position_space.shape) # Two-dimensional regular grid with inhomogeneous exposure position_space = ift.RGSpace([512, 512]) # # Sphere with with uniform exposure # position_space = ift.HPSpace(128) # exposure = ift.Field.full(position_space, 1.) # Defining harmonic space and transform harmonic_space = position_space.get_default_codomain() HT = ift.HarmonicTransformOperator(harmonic_space, position_space) domain = ift.MultiDomain.make({'xi': harmonic_space}) position = ift.from_random('normal', domain) # Define power spectrum and amplitudes def sqrtpspec(k): return 1. / (20. + k**2) p_space = ift.PowerSpace(harmonic_space) pd = ift.PowerDistributor(harmonic_space, p_space) a = ift.PS_field(p_space, sqrtpspec) A = pd(a) # Set up a sky model xi = ift.Variable(position)['xi'] logsky_h = xi * A logsky = HT(logsky_h) sky = ift.PointwisePositiveTanh(logsky) GR = ift.GeometryRemover(position_space) # Set up instrumental response R = GR # Generate mock data d_space = R.target[0] p = R(sky) mock_position = ift.from_random('normal', p.position.domain) pp = p.at(mock_position).value data = np.random.binomial(1, pp.to_global_data().astype(np.float64)) data = ift.Field.from_global_data(d_space, data) # Compute likelihood and Hamiltonian position = ift.from_random('normal', p.position.domain) likelihood = ift.BernoulliEnergy(p, data) ic_cg = ift.GradientNormController(iteration_limit=50) ic_newton = ift.GradientNormController(name='Newton', iteration_limit=30, tol_abs_gradnorm=1e-3) minimizer = ift.RelaxedNewton(ic_newton) ic_sampling = ift.GradientNormController(iteration_limit=100) # Minimize the Hamiltonian H = ift.Hamiltonian(likelihood, ic_sampling) H = H.make_invertible(ic_cg) # minimizer = ift.SteepestDescent(ic_newton) H, convergence = minimizer(H) reconstruction = sky.at(H.position).value ift.plot(reconstruction, title='reconstruction') ift.plot(GR.adjoint_times(data), title='data') ift.plot(sky.at(mock_position).value, title='truth') ift.plot_finish(nx=3, xsize=16, ysize=5, title="results", name="bernoulli.png")