amplitude_model.py 4.93 KB
 Martin Reinecke committed Jul 09, 2018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ``````# 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. `````` Martin Reinecke committed Jul 09, 2018 19 20 ``````from __future__ import absolute_import, division, print_function from ..compat import * `````` Philipp Arras committed Jun 27, 2018 21 ``````import numpy as np `````` Martin Reinecke committed Jul 02, 2018 22 23 ``````from ..domains.power_space import PowerSpace from ..domains.unstructured_domain import UnstructuredDomain `````` Philipp Arras committed Jun 27, 2018 24 ``````from ..field import Field `````` Martin Reinecke committed Jul 02, 2018 25 ``````from ..multi.multi_field import MultiField `````` Philipp Arras committed Jun 27, 2018 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 ``````from ..sugar import makeOp, sqrt def _ceps_kernel(dof_space, k, a, k0): return a**2/(1+(k/(k0*dof_space.bindistances[0]))**2)**2 def make_amplitude_model(s_space, Npixdof, ceps_a, ceps_k, sm, sv, im, iv, keys=['tau', 'phi']): ''' Method for construction of amplitude model Computes a smooth power spectrum. Output lives in PowerSpace. Parameters ---------- Npixdof : #pix in dof_space `````` Martin Reinecke committed Jul 02, 2018 45 `````` ceps_a, ceps_k0 : Smoothness parameters in ceps_kernel `````` Philipp Arras committed Jun 27, 2018 46 47 48 `````` eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2 a = ceps_a, k0 = ceps_k0 `````` Martin Reinecke committed Jul 02, 2018 49 `````` sm, sv : slope_mean = expected exponent of power law (e.g. -4), `````` Philipp Arras committed Jun 27, 2018 50 51 52 53 `````` slope_variance (default=1) im, iv : y-intercept_mean, y-intercept_variance of power_slope ''' `````` Martin Reinecke committed Jul 03, 2018 54 55 56 57 58 59 60 `````` from ..operators.exp_transform import ExpTransform from ..operators.qht_operator import QHTOperator from ..operators.slope_operator import SlopeOperator from ..operators.symmetrizing_operator import SymmetrizingOperator from ..models.variable import Variable from ..models.constant import Constant from ..models.local_nonlinearity import PointwiseExponential `````` Philipp Arras committed Jun 27, 2018 61 `````` `````` Philipp Arras committed Jun 27, 2018 62 63 64 65 66 67 68 69 70 71 72 73 74 `````` h_space = s_space.get_default_codomain() p_space = PowerSpace(h_space) exp_transform = ExpTransform(p_space, Npixdof) logk_space = exp_transform.domain[0] dof_space = logk_space.get_default_codomain() param_space = UnstructuredDomain(2) qht = QHTOperator(dof_space, logk_space) sym = SymmetrizingOperator(logk_space) phi_mean = np.array([sm, im]) phi_sig = np.array([sv, iv]) slope = SlopeOperator(param_space, logk_space, phi_sig) `````` 75 `````` norm_phi_mean = Field.from_global_data(param_space, phi_mean/phi_sig) `````` Philipp Arras committed Jun 27, 2018 76 77 78 79 `````` fields = {keys[0]: Field.from_random('normal', dof_space), keys[1]: Field.from_random('normal', param_space)} `````` Martin Reinecke committed Jul 07, 2018 80 `````` position = MultiField.from_dict(fields) `````` Philipp Arras committed Jun 27, 2018 81 82 83 84 85 86 87 88 `````` dof_space = position[keys[0]].domain[0] kern = lambda k: _ceps_kernel(dof_space, k, ceps_a, ceps_k) cepstrum = create_cepstrum_amplitude_field(dof_space, kern) ceps = makeOp(sqrt(cepstrum)) smooth_op = sym * qht * ceps smooth_spec = smooth_op(Variable(position)[keys[0]]) `````` Philipp Arras committed Jun 27, 2018 89 `````` phi = Variable(position)[keys[1]] + Constant(position, norm_phi_mean) `````` Philipp Arras committed Jun 27, 2018 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 `````` linear_spec = slope(phi) loglog_spec = smooth_spec + linear_spec xlog_ampl = PointwiseExponential(0.5*loglog_spec) internals = {'loglog_spec': loglog_spec, 'qht': qht, 'ceps': ceps, 'norm_phi_mean': norm_phi_mean} return exp_transform(xlog_ampl), internals def create_cepstrum_amplitude_field(domain, cepstrum): """Creates a ... Writes the sum of all modes into the zero-mode. Parameters ---------- domain: ??? ??? cepstrum: Callable ??? """ dim = len(domain.shape) dist = domain.bindistances shape = domain.shape # Prepare q_array q_array = np.zeros((dim,) + shape) if dim == 1: `````` 120 `````` ks = domain.get_k_length_array().to_global_data() `````` Philipp Arras committed Jun 27, 2018 121 122 123 124 125 `````` q_array = np.array([ks]) else: for i in range(dim): ks = np.minimum(shape[i] - np.arange(shape[i]) + 1, np.arange(shape[i])) * dist[i] `````` Martin Reinecke committed Jul 08, 2018 126 `````` q_array[i] += ks.reshape((1,)*i + (shape[i],) + (1,)*(dim-i-1)) `````` Philipp Arras committed Jun 27, 2018 127 128 129 130 131 132 133 134 135 136 `````` # Fill cepstrum field (all non-zero modes) no_zero_modes = (slice(1, None),) * dim ks = q_array[(slice(None),) + no_zero_modes] cepstrum_field = np.zeros(shape) cepstrum_field[no_zero_modes] = cepstrum(ks) # Fill cepstrum field (zero-mode subspaces) for i in range(dim): # Prepare indices `````` Martin Reinecke committed Jul 08, 2018 137 138 139 `````` fst_dims = (slice(None),)*i sl = fst_dims + (slice(1, None),) sl2 = fst_dims + (0,) `````` Philipp Arras committed Jun 27, 2018 140 141 142 143 `````` # Do summation cepstrum_field[sl2] = np.sum(cepstrum_field[sl], axis=i) `````` 144 `` return Field.from_global_data(domain, cepstrum_field)``