# 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 .
#
# Copyright(C) 2013-2017 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
from nifty import Space,\
PowerSpace,\
Field,\
ComposedOperator,\
DiagonalOperator,\
FFTOperator,\
sqrt,\
nifty_configuration
__all__ = ['create_power_operator',
'generate_posterior_sample',
'create_composed_fft_operator']
def create_power_operator(domain, power_spectrum, dtype=None,
distribution_strategy=None):
""" Creates a diagonal operator with the given power spectrum.
Constructs a diagonal operator that lives over the specified domain.
Parameters
----------
domain : DomainObject
Domain over which the power operator shall live.
power_spectrum : (array-like, method)
An array-like object, or a method that implements the square root
of a power spectrum as a function of k.
dtype : type *optional*
dtype that the field holding the power spectrum shall use
(default : None).
if dtype == None: the dtype of `power_spectrum` will be used.
distribution_strategy : string *optional*
Distributed strategy to be used by the underlying d2o objects.
(default : 'not')
Returns
-------
DiagonalOperator : An operator that implements the given power spectrum.
"""
if distribution_strategy is None:
distribution_strategy = \
nifty_configuration['default_distribution_strategy']
if isinstance(power_spectrum, Field):
power_domain = power_spectrum.domain
else:
power_domain = PowerSpace(domain,
distribution_strategy=distribution_strategy)
fp = Field(power_domain, val=power_spectrum, dtype=dtype,
distribution_strategy='not')
f = fp.power_synthesize(mean=1, std=0, real_signal=False,
distribution_strategy=distribution_strategy)
# MR FIXME: we need the real part here. Could this also be achieved
# by setting real_signal=True in the call above?
f = f.real
f **= 2
return DiagonalOperator(domain, diagonal=f, bare=True)
def generate_posterior_sample(mean, covariance):
""" Generates a posterior sample from a Gaussian distribution with given
mean and covariance
This method generates samples by setting up the observation and
reconstruction of a mock signal in order to obtain residuals of the right
correlation which are added to the given mean.
Parameters
----------
mean : Field
the mean of the posterior Gaussian distribution
covariance : WienerFilterCurvature
The posterior correlation structure consisting of a
response operator, noise covariance and prior signal covariance
Returns
-------
sample : Field
Returns the a sample from the Gaussian of given mean and covariance.
"""
S = covariance.S
R = covariance.R
N = covariance.N
power = S.diagonal().power_analyze()**.5
mock_signal = power.power_synthesize(real_signal=True)
noise = N.diagonal(bare=True).val
mock_noise = Field.from_random(random_type="normal", domain=N.domain,
std=sqrt(noise), dtype=noise.dtype)
mock_data = R(mock_signal) + mock_noise
mock_j = R.adjoint_times(N.inverse_times(mock_data))
mock_m = covariance.inverse_times(mock_j)
sample = mock_signal - mock_m + mean
return sample
def create_composed_fft_operator(domain, codomain=None, all_to='other'):
fft_op_list = []
space_index_list = []
if codomain is None:
codomain = [None]*len(domain)
for i in range(len(domain)):
space = domain[i]
cospace = codomain[i]
if not isinstance(space, Space):
continue
if (all_to == 'other' or
(all_to == 'position' and space.harmonic) or
(all_to == 'harmonic' and not space.harmonic)):
fft_op_list += [FFTOperator(domain=space, target=cospace)]
space_index_list += [i]
result = ComposedOperator(fft_op_list, default_spaces=space_index_list)
return result