energy_operators.py 14.8 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
Martin Reinecke's avatar
Martin Reinecke committed
15
#
16
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
Martin Reinecke's avatar
Martin Reinecke committed
17

Philipp Arras's avatar
Philipp Arras committed
18
19
import numpy as np

Philipp Arras's avatar
Philipp Arras committed
20
from .. import utilities
Martin Reinecke's avatar
Martin Reinecke committed
21
from ..domain_tuple import DomainTuple
22
from ..multi_domain import MultiDomain
Philipp Arras's avatar
Philipp Arras committed
23
from ..field import Field
24
from ..multi_field import MultiField
Philipp Arras's avatar
Philipp Arras committed
25
from ..linearization import Linearization
Philipp Arras's avatar
Philipp Arras committed
26
27
from ..sugar import makeDomain, makeOp
from .linear_operator import LinearOperator
Martin Reinecke's avatar
Martin Reinecke committed
28
from .operator import Operator
Martin Reinecke's avatar
fix    
Martin Reinecke committed
29
from .sampling_enabler import SamplingEnabler
Philipp Arras's avatar
Philipp Arras committed
30
from .sandwich_operator import SandwichOperator
31
from .scaling_operator import ScalingOperator
32
from .simple_linear_operators import VdotOperator, FieldAdapter
Martin Reinecke's avatar
Martin Reinecke committed
33
34
35


class EnergyOperator(Operator):
Philipp Arras's avatar
Philipp Arras committed
36
    """Operator which has a scalar domain as target domain.
37

Martin Reinecke's avatar
Martin Reinecke committed
38
    It is intended as an objective function for field inference.
39

Philipp Arras's avatar
Philipp Arras committed
40
41
42
    Examples
    --------
     - Information Hamiltonian, i.e. negative-log-probabilities.
Martin Reinecke's avatar
Martin Reinecke committed
43
     - Gibbs free energy, i.e. an averaged Hamiltonian, aka Kullback-Leibler
Philipp Arras's avatar
Philipp Arras committed
44
       divergence.
45
    """
Martin Reinecke's avatar
Martin Reinecke committed
46
47
48
    _target = DomainTuple.scalar_domain()


49
50
class Squared2NormOperator(EnergyOperator):
    """Computes the square of the L2-norm of the output of an operator.
51

Philipp Arras's avatar
Philipp Arras committed
52
53
54
    Parameters
    ----------
    domain : Domain, DomainTuple or tuple of Domain
55
        Domain of the operator in which the L2-norm shall be computed.
Martin Reinecke's avatar
Martin Reinecke committed
56
    """
Philipp Arras's avatar
Philipp Arras committed
57

Martin Reinecke's avatar
Martin Reinecke committed
58
59
60
61
    def __init__(self, domain):
        self._domain = domain

    def apply(self, x):
62
        self._check_input(x)
Martin Reinecke's avatar
Martin Reinecke committed
63
        if isinstance(x, Linearization):
Martin Reinecke's avatar
Martin Reinecke committed
64
            val = Field.scalar(x.val.vdot(x.val))
Martin Reinecke's avatar
Martin Reinecke committed
65
            jac = VdotOperator(2*x.val)(x.jac)
66
            return x.new(val, jac)
Martin Reinecke's avatar
Martin Reinecke committed
67
        return Field.scalar(x.vdot(x))
Martin Reinecke's avatar
Martin Reinecke committed
68

Martin Reinecke's avatar
Martin Reinecke committed
69

Martin Reinecke's avatar
Martin Reinecke committed
70
class QuadraticFormOperator(EnergyOperator):
Philipp Arras's avatar
Philipp Arras committed
71
    """Computes the L2-norm of a Field or MultiField with respect to a
72
    specific kernel given by `endo`.
Philipp Arras's avatar
Philipp Arras committed
73
74
75

    .. math ::
        E(f) = \\frac12 f^\\dagger \\text{endo}(f)
76
77
78

    Parameters
    ----------
Philipp Arras's avatar
Philipp Arras committed
79
    endo : EndomorphicOperator
80
         Kernel of the quadratic form
Martin Reinecke's avatar
Martin Reinecke committed
81
    """
Philipp Arras's avatar
Philipp Arras committed
82
83

    def __init__(self, endo):
Martin Reinecke's avatar
Martin Reinecke committed
84
        from .endomorphic_operator import EndomorphicOperator
Philipp Arras's avatar
Philipp Arras committed
85
        if not isinstance(endo, EndomorphicOperator):
Martin Reinecke's avatar
Martin Reinecke committed
86
            raise TypeError("op must be an EndomorphicOperator")
Philipp Arras's avatar
Philipp Arras committed
87
88
        self._op = endo
        self._domain = endo.domain
Martin Reinecke's avatar
Martin Reinecke committed
89
90

    def apply(self, x):
91
        self._check_input(x)
Martin Reinecke's avatar
Martin Reinecke committed
92
        if isinstance(x, Linearization):
Martin Reinecke's avatar
Martin Reinecke committed
93
94
            t1 = self._op(x.val)
            jac = VdotOperator(t1)(x.jac)
Martin Reinecke's avatar
Martin Reinecke committed
95
            val = Field.scalar(0.5*x.val.vdot(t1))
96
            return x.new(val, jac)
Martin Reinecke's avatar
Martin Reinecke committed
97
        return Field.scalar(0.5*x.vdot(self._op(x)))
Martin Reinecke's avatar
Martin Reinecke committed
98

Philipp Arras's avatar
Philipp Arras committed
99

100
101
102
class VariableCovarianceGaussianEnergy(EnergyOperator):
    """Computes a negative-log Gaussian with unknown covariance.

103
    Represents up to constants in :math:`s`:
104
105

    .. math ::
106
        E(f) = - \\log G(s, D) = 0.5 (s)^\\dagger D^{-1} (s) + 0.5 tr log(D),
107
108

    an information energy for a Gaussian distribution with residual s and
109
    diagonal covariance D.
110
111
112

    Parameters
    ----------
113
    domain : Domain, DomainTuple, tuple of Domain
Philipp Arras's avatar
Philipp Arras committed
114
        Operator domain.
115

116
    residual : key
Philipp Arras's avatar
Philipp Arras committed
117
        Residual key of the Gaussian.
118

Philipp Arras's avatar
Philipp Arras committed
119
    inverse_covariance : key
120
        Inverse covariance diagonal key of the Gaussian.
121
122
    """

Philipp Arras's avatar
Philipp Arras committed
123
124
125
126
127
    def __init__(self, domain, residual_key, inverse_covariance_key):
        self._r = str(residual_key)
        self._icov = str(inverse_covariance_key)
        dom = DomainTuple.make(domain)
        self._domain = MultiDomain.make({self._r: dom, self._icov: dom})
128
129
130

    def apply(self, x):
        self._check_input(x)
Philipp Arras's avatar
Fixup    
Philipp Arras committed
131
        res0 = x[self._r].vdot(x[self._r]*x[self._icov]).real
Philipp Arras's avatar
Philipp Arras committed
132
133
134
135
        res1 = x[self._icov].log().sum()
        res = 0.5*(res0-res1)
        mf = {self._r: x.val[self._icov], self._icov: .5*x.val[self._icov]**(-2)}
        metric = makeOp(MultiField.from_dict(mf))
Philipp Arras's avatar
Fixup    
Philipp Arras committed
136
        return res.add_metric(SandwichOperator.make(x.jac, metric))
137

Martin Reinecke's avatar
Martin Reinecke committed
138
139

class GaussianEnergy(EnergyOperator):
Philipp Arras's avatar
Docs    
Philipp Arras committed
140
    """Computes a negative-log Gaussian.
141

Philipp Arras's avatar
Philipp Arras committed
142
    Represents up to constants in :math:`m`:
Martin Reinecke's avatar
Martin Reinecke committed
143

Philipp Arras's avatar
Philipp Arras committed
144
145
    .. math ::
        E(f) = - \\log G(f-m, D) = 0.5 (f-m)^\\dagger D^{-1} (f-m),
Martin Reinecke's avatar
cleanup    
Martin Reinecke committed
146

Philipp Arras's avatar
Philipp Arras committed
147
148
    an information energy for a Gaussian distribution with mean m and
    covariance D.
149

Philipp Arras's avatar
Philipp Arras committed
150
151
152
153
    Parameters
    ----------
    mean : Field
        Mean of the Gaussian. Default is 0.
154
155
    inverse_covariance : LinearOperator
        Inverse covariance of the Gaussian. Default is the identity operator.
Philipp Arras's avatar
Fixup    
Philipp Arras committed
156
    domain : Domain, DomainTuple, tuple of Domain or MultiDomain
Philipp Arras's avatar
Philipp Arras committed
157
158
159
160
161
162
        Operator domain. By default it is inferred from `mean` or
        `covariance` if specified

    Note
    ----
    At least one of the arguments has to be provided.
Martin Reinecke's avatar
Martin Reinecke committed
163
    """
Martin Reinecke's avatar
Martin Reinecke committed
164

165
    def __init__(self, mean=None, inverse_covariance=None, domain=None):
Martin Reinecke's avatar
Martin Reinecke committed
166
167
        if mean is not None and not isinstance(mean, (Field, MultiField)):
            raise TypeError
168
        if inverse_covariance is not None and not isinstance(inverse_covariance, LinearOperator):
Philipp Arras's avatar
Philipp Arras committed
169
170
            raise TypeError

Martin Reinecke's avatar
Martin Reinecke committed
171
172
173
        self._domain = None
        if mean is not None:
            self._checkEquivalence(mean.domain)
174
175
        if inverse_covariance is not None:
            self._checkEquivalence(inverse_covariance.domain)
Martin Reinecke's avatar
Martin Reinecke committed
176
177
178
179
180
        if domain is not None:
            self._checkEquivalence(domain)
        if self._domain is None:
            raise ValueError("no domain given")
        self._mean = mean
181
        if inverse_covariance is None:
182
            self._op = Squared2NormOperator(self._domain).scale(0.5)
Martin Reinecke's avatar
Martin Reinecke committed
183
        else:
184
185
            self._op = QuadraticFormOperator(inverse_covariance)
        self._icov = None if inverse_covariance is None else inverse_covariance
Martin Reinecke's avatar
Martin Reinecke committed
186
187

    def _checkEquivalence(self, newdom):
Martin Reinecke's avatar
fix    
Martin Reinecke committed
188
        newdom = makeDomain(newdom)
Martin Reinecke's avatar
Martin Reinecke committed
189
        if self._domain is None:
Philipp Arras's avatar
Philipp Arras committed
190
            self._domain = newdom
Martin Reinecke's avatar
Martin Reinecke committed
191
        else:
Philipp Arras's avatar
Philipp Arras committed
192
            if self._domain != newdom:
Martin Reinecke's avatar
Martin Reinecke committed
193
194
195
                raise ValueError("domain mismatch")

    def apply(self, x):
196
        self._check_input(x)
Philipp Arras's avatar
Philipp Arras committed
197
        residual = x if self._mean is None else x - self._mean
Philipp Arras's avatar
Changes    
Philipp Arras committed
198
        res = self._op(residual).real
199
        if not isinstance(x, Linearization) or not x.want_metric:
Martin Reinecke's avatar
Martin Reinecke committed
200
201
202
203
204
205
            return res
        metric = SandwichOperator.make(x.jac, self._icov)
        return res.add_metric(metric)


class PoissonianEnergy(EnergyOperator):
Philipp Arras's avatar
Docs    
Philipp Arras committed
206
207
    """Computes likelihood Hamiltonians of expected count field constrained by
    Poissonian count data.
208

Philipp Arras's avatar
Philipp Arras committed
209
    Represents up to an f-independent term :math:`log(d!)`:
210

Philipp Arras's avatar
Philipp Arras committed
211
212
    .. math ::
        E(f) = -\\log \\text{Poisson}(d|f) = \\sum f - d^\\dagger \\log(f),
213

Philipp Arras's avatar
Philipp Arras committed
214
    where f is a :class:`Field` in data space with the expectation values for
Martin Reinecke's avatar
Martin Reinecke committed
215
    the counts.
Philipp Arras's avatar
Philipp Arras committed
216
217
218
219
220
221

    Parameters
    ----------
    d : Field
        Data field with counts. Needs to have integer dtype and all field
        values need to be non-negative.
Martin Reinecke's avatar
Martin Reinecke committed
222
    """
Philipp Arras's avatar
Philipp Arras committed
223

224
    def __init__(self, d):
Philipp Arras's avatar
Philipp Arras committed
225
226
        if not isinstance(d, Field) or not np.issubdtype(d.dtype, np.integer):
            raise TypeError
Martin Reinecke's avatar
stage2    
Martin Reinecke committed
227
        if np.any(d.val < 0):
Philipp Arras's avatar
Philipp Arras committed
228
            raise ValueError
229
230
        self._d = d
        self._domain = DomainTuple.make(d.domain)
Martin Reinecke's avatar
Martin Reinecke committed
231
232

    def apply(self, x):
233
        self._check_input(x)
Martin Reinecke's avatar
Martin Reinecke committed
234
        res = x.sum()
Martin Reinecke's avatar
stage2    
Martin Reinecke committed
235
        tmp = res.val.val if isinstance(res, Linearization) else res
Martin Reinecke's avatar
Martin Reinecke committed
236
237
        # if we have no infinity here, we can continue with the calculation;
        # otherwise we know that the result must also be infinity
Martin Reinecke's avatar
Martin Reinecke committed
238
        if not np.isinf(tmp):
Martin Reinecke's avatar
Martin Reinecke committed
239
            res = res - x.log().vdot(self._d)
Martin Reinecke's avatar
Martin Reinecke committed
240
        if not isinstance(x, Linearization):
Martin Reinecke's avatar
Martin Reinecke committed
241
            return Field.scalar(res)
242
243
        if not x.want_metric:
            return res
Martin Reinecke's avatar
Martin Reinecke committed
244
245
246
        metric = SandwichOperator.make(x.jac, makeOp(1./x.val))
        return res.add_metric(metric)

247

248
class InverseGammaLikelihood(EnergyOperator):
Philipp Arras's avatar
Docs    
Philipp Arras committed
249
    """Computes the negative log-likelihood of the inverse gamma distribution.
250
251
252

    It negative log-pdf(x) is given by

Martin Reinecke's avatar
Martin Reinecke committed
253
254
255
256
257
258
259
    .. math ::

        \\sum_i (\\alpha_i+1)*\\ln(x_i) + \\beta_i/x_i

    This is the likelihood for the variance :math:`x=S_k` given data
    :math:`\\beta = 0.5 |s_k|^2` where the Field :math:`s` is known to have
    the covariance :math:`S_k`.
260
261
262
263
264
265
266

    Parameters
    ----------
    beta : Field
        beta parameter of the inverse gamma distribution
    alpha : Scalar, Field, optional
        alpha parameter of the inverse gamma distribution
267
    """
Philipp Arras's avatar
Philipp Arras committed
268

269
270
    def __init__(self, beta, alpha=-0.5):
        if not isinstance(beta, Field):
Philipp Arras's avatar
Philipp Arras committed
271
            raise TypeError
272
273
        self._beta = beta
        if np.isscalar(alpha):
Martin Reinecke's avatar
stage2    
Martin Reinecke committed
274
            alpha = Field(beta.domain, np.full(beta.shape, alpha))
275
276
277
278
        elif not isinstance(alpha, Field):
            raise TypeError
        self._alphap1 = alpha+1
        self._domain = DomainTuple.make(beta.domain)
279
280

    def apply(self, x):
281
        self._check_input(x)
282
        res = x.log().vdot(self._alphap1) + (1./x).vdot(self._beta)
283
284
        if not isinstance(x, Linearization):
            return Field.scalar(res)
285
286
        if not x.want_metric:
            return res
287
        metric = SandwichOperator.make(x.jac, makeOp(self._alphap1/(x.val**2)))
288
289
290
        return res.add_metric(metric)


291
class StudentTEnergy(EnergyOperator):
Lukas Platz's avatar
Lukas Platz committed
292
    """Computes likelihood energy corresponding to Student's t-distribution.
293
294

    .. math ::
Lukas Platz's avatar
Lukas Platz committed
295
296
        E_\\theta(f) = -\\log \\text{StudentT}_\\theta(f)
                     = \\frac{\\theta + 1}{2} \\log(1 + \\frac{f^2}{\\theta}),
297

Lukas Platz's avatar
Lukas Platz committed
298
    where f is a field defined on `domain`.
299
300
301

    Parameters
    ----------
Lukas Platz's avatar
Lukas Platz committed
302
303
    domain : `Domain` or `DomainTuple`
        Domain of the operator
304
305
306
307
308
309
310
311
312
313
    theta : Scalar
        Degree of freedom parameter for the student t distribution
    """

    def __init__(self, domain, theta):
        self._domain = DomainTuple.make(domain)
        self._theta = theta

    def apply(self, x):
        self._check_input(x)
314
        v = ((self._theta+1)/2)*(x**2/self._theta).log1p().sum()
315
316
317
318
        if not isinstance(x, Linearization):
            return Field.scalar(v)
        if not x.want_metric:
            return v
319
        met = ScalingOperator(self.domain, (self._theta+1) / (self._theta+3))
320
321
322
323
        met = SandwichOperator.make(x.jac, met)
        return v.add_metric(met)


Martin Reinecke's avatar
Martin Reinecke committed
324
class BernoulliEnergy(EnergyOperator):
Philipp Arras's avatar
Philipp Arras committed
325
    """Computes likelihood energy of expected event frequency constrained by
326
327
    event data.

Philipp Arras's avatar
Philipp Arras committed
328
329
330
331
332
333
334
    .. math ::
        E(f) = -\\log \\text{Bernoulli}(d|f)
             = -d^\\dagger \\log f  - (1-d)^\\dagger \\log(1-f),

    where f is a field defined on `d.domain` with the expected
    frequencies of events.

335
336
    Parameters
    ----------
Martin Reinecke's avatar
Martin Reinecke committed
337
    d : Field
Philipp Arras's avatar
Philipp Arras committed
338
        Data field with events (1) or non-events (0).
Martin Reinecke's avatar
Martin Reinecke committed
339
    """
Philipp Arras's avatar
Philipp Arras committed
340

341
    def __init__(self, d):
Philipp Arras's avatar
Philipp Arras committed
342
343
        if not isinstance(d, Field) or not np.issubdtype(d.dtype, np.integer):
            raise TypeError
Martin Reinecke's avatar
stage2    
Martin Reinecke committed
344
        if not np.all(np.logical_or(d.val == 0, d.val == 1)):
Philipp Arras's avatar
Philipp Arras committed
345
            raise ValueError
Martin Reinecke's avatar
Martin Reinecke committed
346
        self._d = d
347
        self._domain = DomainTuple.make(d.domain)
Martin Reinecke's avatar
Martin Reinecke committed
348
349

    def apply(self, x):
350
        self._check_input(x)
Philipp Arras's avatar
Philipp Arras committed
351
        v = -(x.log().vdot(self._d) + (1. - x).log().vdot(1. - self._d))
Martin Reinecke's avatar
Martin Reinecke committed
352
        if not isinstance(x, Linearization):
Martin Reinecke's avatar
Martin Reinecke committed
353
            return Field.scalar(v)
354
355
        if not x.want_metric:
            return v
Philipp Arras's avatar
Philipp Arras committed
356
        met = makeOp(1./(x.val*(1. - x.val)))
Martin Reinecke's avatar
Martin Reinecke committed
357
358
359
360
        met = SandwichOperator.make(x.jac, met)
        return v.add_metric(met)


361
class StandardHamiltonian(EnergyOperator):
Philipp Arras's avatar
Philipp Arras committed
362
363
    """Computes an information Hamiltonian in its standard form, i.e. with the
    prior being a Gaussian with unit covariance.
364

Philipp Arras's avatar
Philipp Arras committed
365
    Let the likelihood energy be :math:`E_{lh}`. Then this operator computes:
366

Philipp Arras's avatar
Philipp Arras committed
367
368
    .. math ::
         H(f) = 0.5 f^\\dagger f + E_{lh}(f):
369

Martin Reinecke's avatar
Martin Reinecke committed
370
    Other field priors can be represented via transformations of a white
371
372
    Gaussian field into a field with the desired prior probability structure.

Martin Reinecke's avatar
Martin Reinecke committed
373
    By implementing prior information this way, the field prior is represented
374
375
376
    by a generative model, from which NIFTy can draw samples and infer a field
    using the Maximum a Posteriori (MAP) or the Variational Bayes (VB) method.

Philipp Arras's avatar
Philipp Arras committed
377
378
379
380
381
382
383
384
    The metric of this operator can be used as covariance for drawing Gaussian
    samples.

    Parameters
    ----------
    lh : EnergyOperator
        The likelihood energy.
    ic_samp : IterationController
385
        Tells an internal :class:`SamplingEnabler` which convergence criterion
Philipp Arras's avatar
Philipp Arras committed
386
387
388
389
390
391
        to use to draw Gaussian samples.

    See also
    --------
    `Encoding prior knowledge in the structure of the likelihood`,
    Jakob Knollmüller, Torsten A. Ensslin,
Martin Reinecke's avatar
Martin Reinecke committed
392
    `<https://arxiv.org/abs/1812.04403>`_
Martin Reinecke's avatar
Martin Reinecke committed
393
    """
Philipp Arras's avatar
Philipp Arras committed
394

395
    def __init__(self, lh, ic_samp=None, _c_inp=None):
Martin Reinecke's avatar
Martin Reinecke committed
396
397
        self._lh = lh
        self._prior = GaussianEnergy(domain=lh.domain)
398
399
        if _c_inp is not None:
            _, self._prior = self._prior.simplify_for_constant_input(_c_inp)
Martin Reinecke's avatar
Martin Reinecke committed
400
        self._ic_samp = ic_samp
Martin Reinecke's avatar
Martin Reinecke committed
401
        self._domain = lh.domain
Martin Reinecke's avatar
Martin Reinecke committed
402
403

    def apply(self, x):
404
        self._check_input(x)
Philipp Arras's avatar
Philipp Arras committed
405
406
407
        if (self._ic_samp is None or not isinstance(x, Linearization)
                or not x.want_metric):
            return self._lh(x) + self._prior(x)
Martin Reinecke's avatar
Martin Reinecke committed
408
        else:
409
            lhx, prx = self._lh(x), self._prior(x)
410
411
            mtr = SamplingEnabler(lhx.metric, prx.metric,
                                  self._ic_samp)
Philipp Arras's avatar
Philipp Arras committed
412
            return (lhx + prx).add_metric(mtr)
Martin Reinecke's avatar
Martin Reinecke committed
413

Philipp Arras's avatar
Philipp Arras committed
414
415
    def __repr__(self):
        subs = 'Likelihood:\n{}'.format(utilities.indent(self._lh.__repr__()))
416
        subs += '\nPrior:\n{}'.format(self._prior)
Martin Reinecke's avatar
Martin Reinecke committed
417
        return 'StandardHamiltonian:\n' + utilities.indent(subs)
Philipp Arras's avatar
Philipp Arras committed
418

419
420
421
422
    def _simplify_for_constant_input_nontrivial(self, c_inp):
        out, lh1 = self._lh.simplify_for_constant_input(c_inp)
        return out, StandardHamiltonian(lh1, self._ic_samp, _c_inp=c_inp)

Martin Reinecke's avatar
Martin Reinecke committed
423

Martin Reinecke's avatar
Martin Reinecke committed
424
class AveragedEnergy(EnergyOperator):
Philipp Arras's avatar
Docs    
Philipp Arras committed
425
    """Averages an energy over samples.
Martin Reinecke's avatar
Martin Reinecke committed
426

427
428
429
    Parameters
    ----------
    h: Hamiltonian
Philipp Arras's avatar
Philipp Arras committed
430
       The energy to be averaged.
Martin Reinecke's avatar
Martin Reinecke committed
431
    res_samples : iterable of Fields
Torsten Ensslin's avatar
Torsten Ensslin committed
432
433
       Set of residual sample points to be added to mean field for
       approximate estimation of the KL.
434

Philipp Arras's avatar
Docs    
Philipp Arras committed
435
436
437
438
439
    Notes
    -----
    - Having symmetrized residual samples, with both :math:`v_i` and
      :math:`-v_i` being present, ensures that the distribution mean is
      exactly represented.
Torsten Ensslin's avatar
Fix te    
Torsten Ensslin committed
440

Philipp Arras's avatar
Docs    
Philipp Arras committed
441
442
443
    - :class:`AveragedEnergy(h)` approximates
      :math:`\\left< H(f) \\right>_{G(f-m,D)}` if the residuals :math:`f-m`
      are drawn from a Gaussian distribution with covariance :math:`D`.
Martin Reinecke's avatar
Martin Reinecke committed
444
    """
Martin Reinecke's avatar
Martin Reinecke committed
445
446
447

    def __init__(self, h, res_samples):
        self._h = h
Martin Reinecke's avatar
Martin Reinecke committed
448
        self._domain = h.domain
Martin Reinecke's avatar
Martin Reinecke committed
449
450
451
        self._res_samples = tuple(res_samples)

    def apply(self, x):
452
        self._check_input(x)
Philipp Arras's avatar
Philipp Arras committed
453
454
        mymap = map(lambda v: self._h(x + v), self._res_samples)
        return utilities.my_sum(mymap)*(1./len(self._res_samples))