# 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 def get_2D_exposure(): x_shape, y_shape = position_space.shape exposure = np.ones(position_space.shape) exposure[x_shape//3:x_shape//2, :] *= 2. exposure[x_shape*4//5:x_shape, :] *= .1 exposure[x_shape//2:x_shape*3//2, :] *= 3. exposure[:, x_shape//3:x_shape//2] *= 2. exposure[:, x_shape*4//5:x_shape] *= .1 exposure[:, x_shape//2:x_shape*3//2] *= 3. exposure = ift.Field.from_global_data(position_space, exposure) return exposure if __name__ == '__main__': # FIXME description of the tutorial 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 = ift.Field.full(position_space, 1.) # Two-dimensional regular grid with inhomogeneous exposure position_space = ift.RGSpace([512, 512]) exposure = get_2D_exposure() # Sphere 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.DomainTuple.make(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 sky = ift.exp(HT(ift.makeOp(A))) M = ift.DiagonalOperator(exposure) GR = ift.GeometryRemover(position_space) # Set up instrumental response R = GR(M) # Generate mock data d_space = R.target[0] lamb = R(sky) mock_position = ift.from_random('normal', domain) data = lamb(mock_position) data = np.random.poisson(data.to_global_data().astype(np.float64)) data = ift.Field.from_global_data(d_space, data) # Compute likelihood and Hamiltonian ic_newton = ift.DeltaEnergyController(name='Newton', iteration_limit=100, tol_rel_deltaE=1e-8) likelihood = ift.PoissonianEnergy(data)(lamb) minimizer = ift.NewtonCG(ic_newton) # Minimize the Hamiltonian H = ift.Hamiltonian(likelihood) H = ift.EnergyAdapter(position, H, want_metric=True) H, convergence = minimizer(H) # Plot results signal = sky(mock_position) reconst = sky(H.position) plot = ift.Plot() plot.add(signal, title='Signal') plot.add(GR.adjoint(data), title='Data') plot.add(reconst, title='Reconstruction') plot.add(reconst - signal, title='Residuals') plot.output(name='getting_started_2.png', xsize=16, ysize=16)