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# 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/>.
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#
# 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.
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import numpy as np

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from . import Space,\
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                  PowerSpace,\
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                  Field,\
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                  ComposedOperator,\
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                  DiagonalOperator,\
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                  FFTOperator,\
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                  sqrt,\
                  nifty_configuration

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__all__ = ['create_power_operator',
           'generate_posterior_sample',
           'create_composed_fft_operator']
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def create_power_operator(domain, power_spectrum, dtype=None,
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                          distribution_strategy=None):
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    """ Creates a diagonal operator with the given power spectrum.
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    Constructs a diagonal operator that lives over the specified domain.
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    Parameters
    ----------
    domain : DomainObject
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        Domain over which the power operator shall live.
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    power_spectrum : (array-like, method)
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        An array-like object, or a method that implements the square root
        of a power spectrum as a function of k.
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    dtype : type *optional*
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        dtype that the field holding the power spectrum shall use
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        (default : None).
        if dtype == None: the dtype of `power_spectrum` will be used.
    distribution_strategy : string *optional*
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        Distributed strategy to be used by the underlying d2o objects.
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        (default : 'not')

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    Returns
    -------
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    DiagonalOperator : An operator that implements the given power spectrum.
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    """
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    if distribution_strategy is None:
        distribution_strategy = \
            nifty_configuration['default_distribution_strategy']

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    if isinstance(power_spectrum, Field):
        power_domain = power_spectrum.domain
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    else:
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        power_domain = PowerSpace(domain,
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                                  distribution_strategy=distribution_strategy)
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    fp = Field(power_domain, val=power_spectrum, dtype=dtype,
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               distribution_strategy='not')
    f = fp.power_synthesize(mean=1, std=0, real_signal=False,
                            distribution_strategy=distribution_strategy)
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    if not issubclass(fp.dtype.type, np.complexfloating):
        f = f.real

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    f **= 2
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    return DiagonalOperator(domain, diagonal=f, bare=True)
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def generate_posterior_sample(mean, covariance):
    """ Generates a posterior sample from a Gaussian distribution with given
    mean and covariance
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    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.
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    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.

    """

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    S = covariance.S
    R = covariance.R
    N = covariance.N
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    power = sqrt(S.diagonal().power_analyze())
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    mock_signal = power.power_synthesize(real_signal=True)

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    noise = N.diagonal(bare=True)
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    mock_noise = Field.from_random(random_type="normal", domain=N.domain,
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                                   dtype=noise.dtype)
    mock_noise *= sqrt(noise)

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    mock_data = R(mock_signal) + mock_noise
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    mock_j = R.adjoint_times(N.inverse_times(mock_data))
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    mock_m = covariance.inverse_times(mock_j)
    sample = mock_signal - mock_m + mean
    return sample
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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