correlated_fields.py 11.6 KB
Newer Older
Martin Reinecke's avatar
Martin Reinecke committed
1
2
3
4
5
6
7
8
9
10
11
12
13
# 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/>.
#
14
# Copyright(C) 2013-2019 Max-Planck-Society
Philipp Arras's avatar
Philipp Arras committed
15
# Authors: Philipp Frank, Philipp Arras
Martin Reinecke's avatar
Martin Reinecke committed
16
#
17
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
Philipp Arras's avatar
Philipp Arras committed
18

Philipp Arras's avatar
Philipp Arras committed
19
import numpy as np
20

Philipp Arras's avatar
Philipp Arras committed
21
from ..domain_tuple import DomainTuple
Philipp Arras's avatar
Philipp Arras committed
22
23
from ..domains.power_space import PowerSpace
from ..domains.unstructured_domain import UnstructuredDomain
24
from ..field import Field
Philipp Arras's avatar
Philipp Arras committed
25
from ..operators.adder import Adder
26
from ..operators.contraction_operator import ContractionOperator
Philipp Arras's avatar
Philipp Arras committed
27
from ..operators.distributors import PowerDistributor
Philipp Arras's avatar
Philipp Arras committed
28
from ..operators.endomorphic_operator import EndomorphicOperator
Martin Reinecke's avatar
Martin Reinecke committed
29
from ..operators.harmonic_operators import HarmonicTransformOperator
Philipp Arras's avatar
Philipp Arras committed
30
from ..operators.linear_operator import LinearOperator
Philipp Arras's avatar
Philipp Arras committed
31
32
from ..operators.operator import Operator
from ..operators.simple_linear_operators import VdotOperator, ducktape
Philipp Arras's avatar
Philipp Arras committed
33
from ..operators.value_inserter import ValueInserter
34
35
from ..sugar import from_global_data, full, makeDomain

Philipp Arras's avatar
Philipp Arras committed
36

37
38
def _lognormal_moments(mean, sig):
    mean, sig = float(mean), float(sig)
Philipp Arras's avatar
Philipp Arras committed
39
40
41
    assert sig > 0
    logsig = np.sqrt(np.log((sig/mean)**2 + 1))
    logmean = np.log(mean) - logsig**2/2
42
43
    return logmean, logsig

44

45
46
47
def _lognormal_moment_matching(mean, sig, key):
    key = str(key)
    logmean, logsig = _lognormal_moments(mean, sig)
Philipp Arras's avatar
Philipp Arras committed
48
49
    return _normal(logmean, logsig, key).exp()

50

Philipp Arras's avatar
Philipp Arras committed
51
52
53
54
55
def _normal(mean, sig, key):
    return Adder(Field.scalar(mean)) @ (
        sig*ducktape(DomainTuple.scalar_domain(), None, key))


Philipp Frank's avatar
Philipp Frank committed
56
class _SlopeRemover(EndomorphicOperator):
57
    def __init__(self, domain, logkl):
Philipp Frank's avatar
Philipp Frank committed
58
        self._domain = makeDomain(domain)
59
        self._sc = logkl/float(logkl[-1])
Philipp Arras's avatar
Philipp Arras committed
60

Philipp Frank's avatar
Philipp Frank committed
61
        self._capability = self.TIMES | self.ADJOINT_TIMES
Philipp Arras's avatar
Philipp Arras committed
62

63
64
    def apply(self, x, mode):
        self._check_input(x, mode)
Philipp Frank's avatar
Philipp Frank committed
65
66
        x = x.to_global_data()
        if mode == self.TIMES:
67
            res = x - x[-1]*self._sc
Philipp Frank's avatar
Philipp Frank committed
68
        else:
69
            res = np.zeros(x.shape, dtype=x.dtype)
Philipp Frank's avatar
Philipp Frank committed
70
71
            res += x
            res[-1] -= (x*self._sc).sum()
72
        return from_global_data(self._tgt(mode), res)
Philipp Frank's avatar
Philipp Frank committed
73

74
75

def _make_slope_Operator(smooth, loglogavgslope):
Philipp Frank's avatar
Philipp Frank committed
76
77
78
79
80
    tg = smooth.target
    logkl = _log_k_lengths(tg[0])
    assert logkl.shape[0] == tg[0].shape[0] - 1
    logkl -= logkl[0]
    logkl = np.insert(logkl, 0, 0)
81
    noslope = _SlopeRemover(tg, logkl) @ smooth
Philipp Frank's avatar
Philipp Frank committed
82

Philipp Frank's avatar
Philipp Frank committed
83
    _t = VdotOperator(from_global_data(tg, logkl)).adjoint
Philipp Frank's avatar
Philipp Frank committed
84
    return _t @ loglogavgslope + noslope
Philipp Arras's avatar
Philipp Arras committed
85

86

Philipp Arras's avatar
Philipp Arras committed
87
88
89
def _log_k_lengths(pspace):
    return np.log(pspace.k_lengths[1:])

90

Philipp Arras's avatar
Philipp Arras committed
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
class _TwoLogIntegrations(LinearOperator):
    def __init__(self, target):
        self._target = makeDomain(target)
        self._domain = makeDomain(
            UnstructuredDomain((2, self.target.shape[0] - 2)))
        self._capability = self.TIMES | self.ADJOINT_TIMES
        if not isinstance(self._target[0], PowerSpace):
            raise TypeError
        logk_lengths = _log_k_lengths(self._target[0])
        self._logvol = logk_lengths[1:] - logk_lengths[:-1]

    def apply(self, x, mode):
        self._check_input(x, mode)
        if mode == self.TIMES:
            x = x.to_global_data()
            res = np.empty(self._target.shape)
            res[0] = 0
            res[1] = 0
            res[2:] = np.cumsum(x[1])
            res[2:] = (res[2:] + res[1:-1])/2*self._logvol + x[0]
            res[2:] = np.cumsum(res[2:])
            return from_global_data(self._target, res)
        else:
            x = x.to_global_data_rw()
            res = np.zeros(self._domain.shape)
            x[2:] = np.cumsum(x[2:][::-1])[::-1]
            res[0] += x[2:]
            x[2:] *= self._logvol/2.
119
120
            x[1:-1] += x[2:]
            res[1] += np.cumsum(x[2:][::-1])[::-1]
Philipp Arras's avatar
Philipp Arras committed
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
            return from_global_data(self._domain, res)


class _Normalization(Operator):
    def __init__(self, domain):
        self._domain = self._target = makeDomain(domain)
        hspace = self._domain[0].harmonic_partner
        pd = PowerDistributor(hspace, power_space=self._domain[0])
        cst = pd.adjoint(full(pd.target, 1.)).to_global_data_rw()
        cst[0] = 0
        self._cst = from_global_data(self._domain, cst)
        self._specsum = _SpecialSum(self._domain)

    def apply(self, x):
        self._check_input(x)
        amp = x.exp()
        spec = (2*x).exp()
        # FIXME This normalizes also the zeromode which is supposed to be left
        # untouched by this operator
        return self._specsum(self._cst*spec)**(-0.5)*amp


class _SpecialSum(EndomorphicOperator):
    def __init__(self, domain):
        self._domain = makeDomain(domain)
        self._capability = self.TIMES | self.ADJOINT_TIMES

    def apply(self, x, mode):
        self._check_input(x, mode)
        return full(self._tgt(mode), x.sum())


153
154
155
class _Amplitude(Operator):
    def __init__(self, target, fluctuations, flexibility, asperity,
                 loglogavgslope, key):
Philipp Arras's avatar
Philipp Arras committed
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
        """
        fluctuations > 0
        flexibility > 0
        asperity > 0
        loglogavgslope probably negative
        """
        assert isinstance(fluctuations, Operator)
        assert isinstance(flexibility, Operator)
        assert isinstance(asperity, Operator)
        assert isinstance(loglogavgslope, Operator)
        target = makeDomain(target)
        assert len(target) == 1
        assert isinstance(target[0], PowerSpace)

        twolog = _TwoLogIntegrations(target)
        dt = twolog._logvol
        sc = np.zeros(twolog.domain.shape)
        sc[0] = sc[1] = np.sqrt(dt)
        sc = from_global_data(twolog.domain, sc)
        expander = VdotOperator(sc).adjoint
        sigmasq = expander @ flexibility

        dist = np.zeros(twolog.domain.shape)
        dist[0] += 1.
        dist = from_global_data(twolog.domain, dist)
        scale = VdotOperator(dist).adjoint @ asperity

        shift = np.ones(scale.target.shape)
        shift[0] = dt**2/12.
        shift = from_global_data(scale.target, shift)
        scale = sigmasq*(Adder(shift) @ scale).sqrt()

        smooth = twolog @ (scale*ducktape(scale.target, None, key))
189
        smoothslope = _make_slope_Operator(smooth, loglogavgslope)
Philipp Arras's avatar
Philipp Arras committed
190
191
192
193
194
195
196
197
198

        normal_ampl = _Normalization(target) @ smoothslope
        vol = target[0].harmonic_partner.get_default_codomain().total_volume
        arr = np.zeros(target.shape)
        arr[1:] = vol
        expander = VdotOperator(from_global_data(target, arr)).adjoint
        mask = np.zeros(target.shape)
        mask[0] = vol
        adder = Adder(from_global_data(target, mask))
199
200
201
202
        self._op = adder @ ((expander @ fluctuations)*normal_ampl)

        self._domain = self._op.domain
        self._target = self._op.target
Philipp Arras's avatar
Philipp Arras committed
203

204
205
206
    def apply(self, x):
        self._check_input(x)
        return self._op(x)
Philipp Arras's avatar
Philipp Arras committed
207

208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223

class CorrelatedFieldMaker:
    def __init__(self):
        self._a = []

    def add_fluctuations(self,
                         target,
                         fluctuations_mean,
                         fluctuations_stddev,
                         flexibility_mean,
                         flexibility_stddev,
                         asperity_mean,
                         asperity_stddev,
                         loglogavgslope_mean,
                         loglogavgslope_stddev,
                         prefix=''):
Philipp Arras's avatar
Philipp Arras committed
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
        fluctuations_mean = float(fluctuations_mean)
        fluctuations_stddev = float(fluctuations_stddev)
        flexibility_mean = float(flexibility_mean)
        flexibility_stddev = float(flexibility_stddev)
        asperity_mean = float(asperity_mean)
        asperity_stddev = float(asperity_stddev)
        loglogavgslope_mean = float(loglogavgslope_mean)
        loglogavgslope_stddev = float(loglogavgslope_stddev)
        prefix = str(prefix)
        assert fluctuations_stddev > 0
        assert fluctuations_mean > 0
        assert flexibility_stddev > 0
        assert flexibility_mean > 0
        assert asperity_stddev > 0
        assert asperity_mean > 0
        assert loglogavgslope_stddev > 0

        fluct = _lognormal_moment_matching(fluctuations_mean,
                                           fluctuations_stddev,
                                           prefix + 'fluctuations')
        flex = _lognormal_moment_matching(flexibility_mean, flexibility_stddev,
                                          prefix + 'flexibility')
        asp = _lognormal_moment_matching(asperity_mean, asperity_stddev,
                                         prefix + 'asperity')
248
        avgsl = _normal(loglogavgslope_mean, loglogavgslope_stddev,
Philipp Arras's avatar
Philipp Arras committed
249
                        prefix + 'loglogavgslope')
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
        self._a.append(
            _Amplitude(target, fluct, flex, asp, avgsl, prefix + 'spectrum'))

    def finalize_from_op(self, zeromode, prefix=''):
        assert isinstance(zeromode, Operator)
        hspace = makeDomain([dd.target[0].harmonic_partner for dd in self._a])
        foo = np.ones(hspace.shape)
        zeroind = len(hspace.shape)*(0,)
        foo[zeroind] = 0
        azm = Adder(from_global_data(hspace, foo)) @ ValueInserter(
            hspace, zeroind) @ zeromode

        n_amplitudes = len(self._a)
        ht = HarmonicTransformOperator(hspace, space=0)
        for i in range(1, n_amplitudes):
            ht = HarmonicTransformOperator(ht.target, space=i) @ ht

        pd = PowerDistributor(hspace, self._a[0].target[0], 0)
        for i in range(1, n_amplitudes):
            foo = PowerDistributor(pd.domain, self._a[i].target[0], space=i)
            pd = pd @ foo

        spaces = tuple(range(n_amplitudes))
        a = ContractionOperator(pd.domain, spaces[1:]).adjoint @ self._a[0]
        for i in range(1, n_amplitudes):
            co = ContractionOperator(pd.domain, spaces[:i] + spaces[(i + 1):])
            a = a*(co.adjoint @ self._a[i])
Philipp Arras's avatar
Philipp Arras committed
277

278
        return ht(azm*(pd @ a)*ducktape(hspace, None, prefix + 'xi'))
Philipp Arras's avatar
Philipp Arras committed
279
280
281
282

    def finalize(self,
                 offset_amplitude_mean,
                 offset_amplitude_stddev,
283
                 prefix='',
Philipp Arras's avatar
Philipp Arras committed
284
285
286
287
288
289
290
291
292
                 offset=None):
        """
        offset vs zeromode: volume factor
        """
        offset_amplitude_stddev = float(offset_amplitude_stddev)
        offset_amplitude_mean = float(offset_amplitude_mean)
        assert offset_amplitude_stddev > 0
        assert offset_amplitude_mean > 0
        if offset is not None:
293
            raise NotImplementedError
Philipp Arras's avatar
Philipp Arras committed
294
295
296
297
            offset = float(offset)
        azm = _lognormal_moment_matching(offset_amplitude_mean,
                                         offset_amplitude_stddev,
                                         prefix + 'zeromode')
298
        return self.finalize_from_op(azm, prefix)
Philipp Arras's avatar
Philipp Arras committed
299
300
301

    @property
    def amplitudes(self):
302
        return self._a
303

304
305
    def effective_total_fluctuation(self,
                                    fluctuations_means,
306
                                    fluctuations_stddevs,
307
                                    nsamples=100):
308
        namps = len(fluctuations_means)
309
310
        xis = np.random.normal(size=namps*nsamples).reshape((namps, nsamples))
        q = np.ones(nsamples)
311
312
313
314
        for i in range(len(fluctuations_means)):
            m, sig = _lognormal_moments(fluctuations_means[i],
                                        fluctuations_stddevs[i])
            f = np.exp(m + sig*xis[i])
315
316
            q *= (1. + f**2)
        q = np.sqrt(q - 1.)
317
        return np.mean(q), np.std(q)