amplitude_model.py 4.99 KB
Newer Older
Martin Reinecke's avatar
Martin Reinecke committed
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 <http://www.gnu.org/licenses/>.
#
# 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.

19
from __future__ import absolute_import, division, print_function
Philipp Arras's avatar
Philipp Arras committed
20

21
import numpy as np
Philipp Arras's avatar
Philipp Arras committed
22
23

from ..compat import *
Martin Reinecke's avatar
Martin Reinecke committed
24
25
from ..domains.power_space import PowerSpace
from ..domains.unstructured_domain import UnstructuredDomain
26
from ..field import Field
Martin Reinecke's avatar
Martin Reinecke committed
27
from ..multi_domain import MultiDomain
Martin Reinecke's avatar
Martin Reinecke committed
28
from ..operators.operator import Operator
Philipp Arras's avatar
Philipp Arras committed
29
from ..sugar import makeOp, sqrt
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54


def _ceps_kernel(dof_space, k, a, k0):
    return a**2/(1+(k/(k0*dof_space.bindistances[0]))**2)**2


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:
55
        ks = domain.get_k_length_array().to_global_data()
56
57
58
59
60
        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's avatar
Martin Reinecke committed
61
            q_array[i] += ks.reshape((1,)*i + (shape[i],) + (1,)*(dim-i-1))
62
63
64
65
66
67
68
69
70
71

    # 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's avatar
Martin Reinecke committed
72
73
74
        fst_dims = (slice(None),)*i
        sl = fst_dims + (slice(1, None),)
        sl2 = fst_dims + (0,)
75
76
77
78

        # Do summation
        cepstrum_field[sl2] = np.sum(cepstrum_field[sl], axis=i)

79
    return Field.from_global_data(domain, cepstrum_field)
Martin Reinecke's avatar
Martin Reinecke committed
80

Martin Reinecke's avatar
Martin Reinecke committed
81

Martin Reinecke's avatar
Martin Reinecke committed
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
class AmplitudeModel(Operator):
    '''
    Computes a smooth power spectrum.
    Output lives in PowerSpace.

    Parameters
    ----------

    Npixdof : #pix in dof_space

    ceps_a, ceps_k0 : Smoothness parameters in ceps_kernel
                        eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2
                        a = ceps_a,  k0 = ceps_k0

    sm, sv : slope_mean = expected exponent of power law (e.g. -4),
                slope_variance (default=1)

    im, iv : y-intercept_mean, y-intercept_variance  of power_slope
    '''
    def __init__(self, s_space, Npixdof, ceps_a, ceps_k, sm, sv, im, iv,
Martin Reinecke's avatar
Martin Reinecke committed
102
                 keys=['tau', 'phi']):
Martin Reinecke's avatar
Martin Reinecke committed
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
        from ..operators.exp_transform import ExpTransform
        from ..operators.qht_operator import QHTOperator
        from ..operators.slope_operator import SlopeOperator
        from ..operators.symmetrizing_operator import SymmetrizingOperator

        h_space = s_space.get_default_codomain()
        p_space = PowerSpace(h_space)
        self._exp_transform = ExpTransform(p_space, Npixdof)
        logk_space = self._exp_transform.domain[0]
        qht = QHTOperator(target=logk_space)
        dof_space = qht.domain[0]
        param_space = UnstructuredDomain(2)
        sym = SymmetrizingOperator(logk_space)

        phi_mean = np.array([sm, im])
        phi_sig = np.array([sv, iv])

        self._slope = SlopeOperator(param_space, logk_space, phi_sig)
Martin Reinecke's avatar
Martin Reinecke committed
121
122
        self._norm_phi_mean = Field.from_global_data(param_space,
                                                     phi_mean/phi_sig)
Martin Reinecke's avatar
Martin Reinecke committed
123

Martin Reinecke's avatar
Martin Reinecke committed
124
125
        self._domain = MultiDomain.make({keys[0]: dof_space,
                                         keys[1]: param_space})
Martin Reinecke's avatar
Martin Reinecke committed
126
        self._target = self._exp_transform.target
Martin Reinecke's avatar
Martin Reinecke committed
127
128
129
130

        kern = lambda k: _ceps_kernel(dof_space, k, ceps_a, ceps_k)
        cepstrum = create_cepstrum_amplitude_field(dof_space, kern)

Martin Reinecke's avatar
Martin Reinecke committed
131
        self._smooth_op = sym(qht(makeOp(sqrt(cepstrum))))
Martin Reinecke's avatar
Martin Reinecke committed
132
133
        self._keys = tuple(keys)

Philipp Arras's avatar
Changes    
Philipp Arras committed
134
135
136
        self._qht = qht
        self._ceps = makeOp(sqrt(cepstrum))

Martin Reinecke's avatar
Martin Reinecke committed
137
    def apply(self, x):
Martin Reinecke's avatar
Martin Reinecke committed
138
139
140
141
142
        smooth_spec = self._smooth_op(x[self._keys[0]])
        phi = x[self._keys[1]] + self._norm_phi_mean
        linear_spec = self._slope(phi)
        loglog_spec = smooth_spec + linear_spec
        return self._exp_transform((0.5*loglog_spec).exp())
Philipp Arras's avatar
Changes    
Philipp Arras committed
143
144
145
146
147
148
149
150

    @property
    def qht(self):
        return self._qht

    @property
    def ceps(self):
        return self._ceps
Philipp Arras's avatar
Philipp Arras committed
151
152
153
154

    @property
    def norm_phi_mean(self):
        return self._norm_phi_mean