# NIFTy
# Copyright (C) 2017 Theo Steininger
#
# Author: Theo Steininger
#
# 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 .
from nifty.operators import EndomorphicOperator,\
FFTOperator,\
InvertibleOperatorMixin
class HarmonicPropagatorOperator(InvertibleOperatorMixin, EndomorphicOperator):
""" NIFTY Harmonic Propagator Operator D.
The propagator operator D, is known from the Wiener Filter.
Its inverse functional form might look like:
D = (S^(-1) + M)^(-1)
D = (S^(-1) + N^(-1))^(-1)
D = (S^(-1) + R^(\dagger) N^(-1) R)^(-1)
In contrast to the PropagatorOperator the inference is done in the
harmonic space.
Parameters
----------
S : LinearOperator
Covariance of the signal prior.
M : LinearOperator
Likelihood contribution.
R : LinearOperator
Response operator translating signal to (noiseless) data.
N : LinearOperator
Covariance of the noise prior or the likelihood, respectively.
inverter : class to invert explicitly defined operators
(default:ConjugateGradient)
preconditioner : Field
numerical preconditioner to speed up convergence
default_spaces : tuple of ints *optional*
Defines on which space(s) of a given field the Operator acts by
default (default: None)
Attributes
----------
domain : tuple of DomainObjects, i.e. Spaces and FieldTypes
The domain on which the Operator's input Field lives.
target : tuple of DomainObjects, i.e. Spaces and FieldTypes
The domain in which the outcome of the operator lives. As the Operator
is endomorphic this is the same as its domain.
unitary : boolean
Indicates whether the Operator is unitary or not.
self_adjoint : boolean
Indicates whether the operator is self_adjoint or not.
Raises
------
ValueError
is raised if
* neither N nor M is given
Notes
-----
Examples
--------
See Also
--------
Scientific reference
https://arxiv.org/abs/0806.3474
"""
# ---Overwritten properties and methods---
def __init__(self, S, M=None, R=None, N=None, inverter=None,
preconditioner=None):
"""
Sets the standard operator properties and `codomain`, `_A1`, `_A2`,
and `RN` if required.
Parameters
----------
S : operator
Covariance of the signal prior.
M : operator
Likelihood contribution.
R : operator
Response operator translating signal to (noiseless) data.
N : operator
Covariance of the noise prior or the likelihood, respectively.
"""
# infer domain, and target
if M is not None:
self._codomain = M.domain
self._likelihood = M.times
elif N is None:
raise ValueError("Either M or N must be given!")
elif R is not None:
self._codomain = R.domain
self._likelihood = \
lambda z: R.adjoint_times(N.inverse_times(R.times(z)))
else:
self._codomain = N.domain
self._likelihood = lambda z: N.inverse_times(z)
self._domain = S.domain
self._S = S
self._fft_S = FFTOperator(self._domain, target=self._codomain)
super(HarmonicPropagatorOperator, self).__init__(inverter=inverter,
preconditioner=preconditioner)
# ---Mandatory properties and methods---
@property
def domain(self):
return self._domain
@property
def self_adjoint(self):
return True
@property
def unitary(self):
return False
# ---Added properties and methods---
def _likelihood_times(self, x, spaces=None):
transformed_x = self._fft_S.times(x, spaces=spaces)
y = self._likelihood(transformed_x)
transformed_y = self._fft_S.adjoint_times(y, spaces=spaces)
result = x.copy_empty()
result.set_val(transformed_y, copy=False)
return result
def _inverse_times(self, x, spaces):
pre_result = self._S.inverse_times(x, spaces)
pre_result += self._likelihood_times(x)
result = x.copy_empty()
result.set_val(pre_result, copy=False)
return result