sugar.py 9.82 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
# 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/>.
Theo Steininger's avatar
Theo Steininger committed
13
#
Martin Reinecke's avatar
Martin Reinecke committed
14
# Copyright(C) 2013-2018 Max-Planck-Society
Theo Steininger's avatar
Theo Steininger committed
15
16
17
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
18

19
import numpy as np
Martin Reinecke's avatar
Martin Reinecke committed
20
21
from .domains.structured_domain import StructuredDomain
from .domains.power_space import PowerSpace
Martin Reinecke's avatar
Martin Reinecke committed
22
23
from .field import Field, sqrt
from .operators.diagonal_operator import DiagonalOperator
Martin Reinecke's avatar
Martin Reinecke committed
24
from .operators.power_distributor import PowerDistributor
25
from .operators.harmonic_transform_operator import HarmonicTransformOperator
Martin Reinecke's avatar
Martin Reinecke committed
26
27
from .domain_tuple import DomainTuple
from . import dobj, utilities
28

Martin Reinecke's avatar
Martin Reinecke committed
29
30
__all__ = ['PS_field',
           'power_analyze',
31
           'power_synthesize',
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
32
           'power_synthesize_nonrandom',
33
           'create_power_field',
34
           'create_power_operator',
35
           'create_composed_ht_operator',
36
           'create_harmonic_smoothing_operator']
37
38


Martin Reinecke's avatar
Martin Reinecke committed
39
40
41
42
43
44
def PS_field(pspace, func, dtype=None):
    if not isinstance(pspace, PowerSpace):
        raise TypeError
    data = dobj.from_global_data(func(pspace.k_lengths))
    return Field(pspace, val=data, dtype=dtype)

Martin Reinecke's avatar
Martin Reinecke committed
45

46
47
def _single_power_analyze(field, idx, binbounds):
    power_domain = PowerSpace(field.domain[idx], binbounds)
Martin Reinecke's avatar
Martin Reinecke committed
48
49
    pd = PowerDistributor(field.domain, power_domain, idx)
    return pd.adjoint_times(field.weight(1)).weight(-1)  # divides by bin size
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65


def power_analyze(field, spaces=None, binbounds=None,
                  keep_phase_information=False):
    """ Computes the square root power spectrum for a subspace of `field`.

    Creates a PowerSpace for the space addressed by `spaces` with the given
    binning and computes the power spectrum as a Field over this
    PowerSpace. This can only be done if the subspace to  be analyzed is a
    harmonic space. The resulting field has the same units as the initial
    field, corresponding to the square root of the power spectrum.

    Parameters
    ----------
    field : Field
        The field to be analyzed
Martin Reinecke's avatar
Martin Reinecke committed
66
67
68
    spaces : None or int or tuple of int , optional
        The set of subdomains for which the powerspectrum shall be computed.
        If None, all subdomains will be converted.
69
        (default : None).
Martin Reinecke's avatar
Martin Reinecke committed
70
    binbounds : None or array-like, optional
71
        Inner bounds of the bins (default : None).
Martin Reinecke's avatar
Martin Reinecke committed
72
73
        if binbounds is None : bins are inferred.
    keep_phase_information : bool, optional
74
75
76
77
78
79
80
81
82
83
84
85
        If False, return a real-valued result containing the power spectrum
        of the input Field.
        If True, return a complex-valued result whose real component
        contains the power spectrum computed from the real part of the
        input Field, and whose imaginary component contains the power
        spectrum computed from the imaginary part of the input Field.
        The absolute value of this result should be identical to the output
        of power_analyze with keep_phase_information=False.
        (default : False).

    Returns
    -------
Martin Reinecke's avatar
Martin Reinecke committed
86
    Field
87
88
89
90
91
92
        The output object. Its domain is a PowerSpace and it contains
        the power spectrum of 'field'.
    """

    for sp in field.domain:
        if not sp.harmonic and not isinstance(sp, PowerSpace):
Martin Reinecke's avatar
Martin Reinecke committed
93
94
            dobj.mprint("WARNING: Field has a space in `domain` which is "
                        "neither harmonic nor a PowerSpace.")
95

96
    spaces = utilities.parse_spaces(spaces, len(field.domain))
97
98
99
100

    if len(spaces) == 0:
        raise ValueError("No space for analysis specified.")

101
102
103
104
    field_real = not np.issubdtype(field.dtype, np.complexfloating)
    if (not field_real) and keep_phase_information:
        raise ValueError("cannot keep phase from real-valued input Field")

105
106
107
    if keep_phase_information:
        parts = [field.real*field.real, field.imag*field.imag]
    else:
108
109
110
111
        if field_real:
            parts = [field**2]
        else:
            parts = [field.real*field.real + field.imag*field.imag]
112
113
114
115
116
117
118
119
120
121

    for space_index in spaces:
        parts = [_single_power_analyze(field=part,
                                       idx=space_index,
                                       binbounds=binbounds)
                 for part in parts]

    return parts[0] + 1j*parts[1] if keep_phase_information else parts[0]


Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
122
def power_synthesize_nonrandom(field, spaces=None):
123
    spaces = utilities.parse_spaces(spaces, len(field.domain))
124
125
126
127
128

    result_domain = list(field.domain)
    spec = sqrt(field)
    for i in spaces:
        result_domain[i] = field.domain[i].harmonic_partner
Martin Reinecke's avatar
Martin Reinecke committed
129
130
        pd = PowerDistributor(result_domain, field.domain[i], i)
        spec = pd(spec)
131
132
133
134
135

    return spec


def power_synthesize(field, spaces=None, real_power=True, real_signal=True):
Martin Reinecke's avatar
Martin Reinecke committed
136
    """Returns a sampled field with `field`**2 as its power spectrum.
137
138
139
140
141
142
143
144

    This method draws a Gaussian random field in the harmonic partner
    domain of this field's domains, using this field as power spectrum.

    Parameters
    ----------
    field : Field
        The input field containing the square root of the power spectrum
Martin Reinecke's avatar
Martin Reinecke committed
145
146
    spaces : None, int, or tuple of int, optional
        Specifies the subdomains containing all the PowerSpaces which
147
        should be converted (default : None).
Martin Reinecke's avatar
Martin Reinecke committed
148
149
        if spaces is None : Tries to convert the whole domain.
    real_power : bool, optional
150
151
        Determines whether the power spectrum is treated as intrinsically
        real or complex (default : True).
Martin Reinecke's avatar
Martin Reinecke committed
152
    real_signal : bool, optional
153
154
155
156
157
        True will result in a purely real signal-space field
        (default : True).

    Returns
    -------
Martin Reinecke's avatar
Martin Reinecke committed
158
    Field
159
160
161
162
163
164
165
166
167
168
169
        The output object. A random field created with the power spectrum
        stored in the `spaces` in `field`.

    Notes
    -----
    For this the spaces specified by `spaces` must be a PowerSpace.
    This expects this field to be the square root of a power spectrum, i.e.
    to have the unit of the field to be sampled.

    Raises
    ------
Martin Reinecke's avatar
Martin Reinecke committed
170
    ValueError : If a domain specified by `spaces` is not a PowerSpace.
171
172
    """

Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
173
    spec = power_synthesize_nonrandom(field, spaces)
174
175
176
    self_real = not np.issubdtype(spec.dtype, np.complexfloating)
    if (not real_power) and self_real:
        raise ValueError("can't draw complex realizations from real spectrum")
177
178
179
180
181

    # create random samples: one or two, depending on whether the
    # power spectrum is real or complex
    result = [field.from_random('normal', mean=0., std=1.,
                                domain=spec.domain,
Martin Reinecke's avatar
Martin Reinecke committed
182
183
                                dtype=np.float64 if real_signal
                                else np.complex128)
184
185
              for x in range(1 if real_power else 2)]

186
    result[0] *= spec if self_real else spec.real
187
188
189
190
191
192
    if not real_power:
        result[1] *= spec.imag

    return result[0] if real_power else result[0] + 1j*result[1]


193
def create_power_field(domain, power_spectrum, dtype=None):
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
194
195
196
197
198
199
200
201
202
203
204
    if not callable(power_spectrum):  # we have a Field living on a PowerSpace
        if not isinstance(power_spectrum, Field):
            raise TypeError("Field object expected")
        if len(power_spectrum.domain) != 1:
            raise ValueError("exactly one domain required")
        if not isinstance(power_spectrum.domain[0], PowerSpace):
            raise TypeError("PowerSpace required")
        power_domain = power_spectrum.domain[0]
        fp = Field(power_domain, val=power_spectrum.val, dtype=dtype)
    else:
        power_domain = PowerSpace(domain)
Martin Reinecke's avatar
Martin Reinecke committed
205
        fp = PS_field(power_domain, power_spectrum, dtype)
206

Martin Reinecke's avatar
Martin Reinecke committed
207
    return PowerDistributor(domain, power_domain)(fp)
208

209

Martin Reinecke's avatar
Martin Reinecke committed
210
def create_power_operator(domain, power_spectrum, space=None, dtype=None):
Theo Steininger's avatar
Theo Steininger committed
211
    """ Creates a diagonal operator with the given power spectrum.
212

213
    Constructs a diagonal operator that lives over the specified domain.
214

215
216
    Parameters
    ----------
Martin Reinecke's avatar
Martin Reinecke committed
217
    domain : Domain, tuple of Domain or DomainTuple
218
        Domain over which the power operator shall live.
Martin Reinecke's avatar
Martin Reinecke committed
219
220
    power_spectrum : callable or Field
        An object that contains the power spectrum as a function of k.
Martin Reinecke's avatar
Martin Reinecke committed
221
    space : int
Martin Reinecke's avatar
Martin Reinecke committed
222
223
        the domain index on which the power operator will work
    dtype : None or type, optional
224
        dtype that the field holding the power spectrum shall use
Theo Steininger's avatar
Theo Steininger committed
225
        (default : None).
Martin Reinecke's avatar
Martin Reinecke committed
226
        if dtype is None: the dtype of `power_spectrum` will be used.
Theo Steininger's avatar
Theo Steininger committed
227

228
229
    Returns
    -------
Martin Reinecke's avatar
Martin Reinecke committed
230
231
    DiagonalOperator
        An operator that implements the given power spectrum.
232
    """
Martin Reinecke's avatar
Martin Reinecke committed
233
234
    domain = DomainTuple.make(domain)
    if space is None:
Martin Reinecke's avatar
Martin Reinecke committed
235
        if len(domain) != 1:
Martin Reinecke's avatar
Martin Reinecke committed
236
237
238
239
            raise ValueError("space keyword must be set")
        else:
            space = 0
    space = int(space)
240
    return DiagonalOperator(
Martin Reinecke's avatar
Martin Reinecke committed
241
        create_power_field(domain[space], power_spectrum, dtype),
Martin Reinecke's avatar
Martin Reinecke committed
242
        domain=domain, spaces=space)
243

244

245
246
247
248
249
def create_composed_ht_operator(domain, codomain=None):
    if codomain is None:
        codomain = [None]*len(domain)
    res = None
    for i, space in enumerate(domain):
Martin Reinecke's avatar
Martin Reinecke committed
250
        if isinstance(space, StructuredDomain) and space.harmonic:
251
252
253
254
255
256
257
258
            tdom = domain if res is None else res.target
            op = HarmonicTransformOperator(tdom, codomain[i], i)
            res = op if res is None else op*res
    if res is None:
        raise ValueError("empty operator")
    return res


259
260
261
262
def create_harmonic_smoothing_operator(domain, space, sigma):
    kfunc = domain[space].get_fft_smoothing_kernel_function(sigma)
    return DiagonalOperator(kfunc(domain[space].get_k_length_array()), domain,
                            space)