# 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.
import numpy as np
from . import Space,\
PowerSpace,\
Field,\
ComposedOperator,\
DiagonalOperator,\
FFTOperator,\
sqrt
__all__ = ['create_power_field',
'create_power_operator',
'generate_posterior_sample',
'create_composed_fft_operator']
def create_power_field(domain, power_spectrum, dtype=None):
if not callable(power_spectrum):
raise TypeError("power_spectrum must be callable")
power_domain = PowerSpace(domain)
fp = Field(power_domain, val=power_spectrum(power_domain.k_lengths),
dtype=dtype)
f = fp.power_synthesize_special()
if not issubclass(fp.dtype.type, np.complexfloating):
f = f.real
f **= 2
return f
def create_power_operator(domain, power_spectrum, dtype=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 : callable
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.
Returns
-------
DiagonalOperator : An operator that implements the given power spectrum.
"""
return DiagonalOperator(create_power_field(domain, power_spectrum, dtype))
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 = sqrt(S.diagonal().weight(1).power_analyze())
mock_signal = power.power_synthesize(real_signal=True)
noise = N.diagonal()
mock_noise = Field.from_random(random_type="normal", domain=N.domain,
dtype=noise.dtype.type)
mock_noise *= sqrt(noise)
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 = []
if codomain is None:
codomain = [None]*len(domain)
interdomain = list(domain.domains)
for i, space in enumerate(domain):
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)):
if codomain[i] is None:
interdomain[i] = domain[i].get_default_codomain()
else:
interdomain[i] = codomain[i]
fft_op_list += [FFTOperator(domain=domain, target=interdomain,
space=i)]
domain = interdomain
return ComposedOperator(fft_op_list)