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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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#
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# Copyright(C) 2013-2018 Max-Planck-Society
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#
# 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 .domains.power_space import PowerSpace
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from .field import Field
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from .operators.diagonal_operator import DiagonalOperator
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from .operators.power_distributor import PowerDistributor
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from .domain_tuple import DomainTuple
from . import dobj, utilities
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from .logger import logger
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__all__ = ['PS_field',
           'power_analyze',
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           'create_power_operator',
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           'create_harmonic_smoothing_operator',
           'get_signal_variance']

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def PS_field(pspace, func):
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    if not isinstance(pspace, PowerSpace):
        raise TypeError
    data = dobj.from_global_data(func(pspace.k_lengths))
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    return Field(pspace, val=data)
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def get_signal_variance(spec, space):
    """
    Computes how much a field with a given power spectrum will vary in space

    This is a small helper function that computes how the expected variance
    of a harmonically transformed sample of this power spectrum.

    Parameters
    ---------
    spec: method
        a method that takes one k-value and returns the power spectrum at that
        location
    space: PowerSpace or any harmonic Domain
        If this function is given a harmonic domain, it creates the naturally binned
        PowerSpace to that domain.
        The field, for which the signal variance is then computed, is assumed to have
        this PowerSpace as naturally binned PowerSpace
    """
    if space.harmonic:
        space = PowerSpace(space)
    if not isinstance(space, PowerSpace):
        raise ValueError("space must be either a harmonic space or Power space.")
    field = PS_field(space, spec)
    dist = PowerDistributor(space.harmonic_partner, space)
    k_field = dist(field)
    return k_field.weight(2).sum()

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def _single_power_analyze(field, idx, binbounds):
    power_domain = PowerSpace(field.domain[idx], binbounds)
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    pd = PowerDistributor(field.domain, power_domain, idx)
    return pd.adjoint_times(field.weight(1)).weight(-1)  # divides by bin size
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# MR FIXME: this function is not well suited for analyzing more than one
# subdomain at once, because it allows only one set of binbounds.
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def power_analyze(field, spaces=None, binbounds=None,
                  keep_phase_information=False):
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    """ Computes the power spectrum for a subspace of `field`.
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    Creates a PowerSpace for the space addressed by `spaces` with the given
    binning and computes the power spectrum as a Field over this
    PowerSpace. This can only be done if the subspace to  be analyzed is a
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    harmonic space. The resulting field has the same units as the square of the
    initial field.
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    Parameters
    ----------
    field : Field
        The field to be analyzed
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    spaces : None or int or tuple of int, optional
        The indices of subdomains for which the power spectrum shall be
        computed.
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        If None, all subdomains will be converted.
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        (default : None).
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    binbounds : None or array-like, optional
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        Inner bounds of the bins (default : None).
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        if binbounds is None : bins are inferred.
    keep_phase_information : bool, optional
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        If False, return a real-valued result containing the power spectrum
        of the input Field.
        If True, return a complex-valued result whose real component
        contains the power spectrum computed from the real part of the
        input Field, and whose imaginary component contains the power
        spectrum computed from the imaginary part of the input Field.
        The absolute value of this result should be identical to the output
        of power_analyze with keep_phase_information=False.
        (default : False).

    Returns
    -------
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    Field
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        The output object. Its domain is a PowerSpace and it contains
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        the power spectrum of `field`.
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    """

    for sp in field.domain:
        if not sp.harmonic and not isinstance(sp, PowerSpace):
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            logger.warning("WARNING: Field has a space in `domain` which is "
                           "neither harmonic nor a PowerSpace.")
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    spaces = utilities.parse_spaces(spaces, len(field.domain))
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    if len(spaces) == 0:
        raise ValueError("No space for analysis specified.")

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    field_real = not np.issubdtype(field.dtype, np.complexfloating)
    if (not field_real) and keep_phase_information:
        raise ValueError("cannot keep phase from real-valued input Field")

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    if keep_phase_information:
        parts = [field.real*field.real, field.imag*field.imag]
    else:
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        if field_real:
            parts = [field**2]
        else:
            parts = [field.real*field.real + field.imag*field.imag]
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    for space_index in spaces:
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        parts = [_single_power_analyze(part, space_index, binbounds)
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                 for part in parts]

    return parts[0] + 1j*parts[1] if keep_phase_information else parts[0]


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def _create_power_field(domain, power_spectrum):
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    if not callable(power_spectrum):  # we have a Field living on a PowerSpace
        if not isinstance(power_spectrum, Field):
            raise TypeError("Field object expected")
        if len(power_spectrum.domain) != 1:
            raise ValueError("exactly one domain required")
        if not isinstance(power_spectrum.domain[0], PowerSpace):
            raise TypeError("PowerSpace required")
        power_domain = power_spectrum.domain[0]
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        fp = Field(power_domain, val=power_spectrum.val)
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    else:
        power_domain = PowerSpace(domain)
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        fp = PS_field(power_domain, power_spectrum)
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    return PowerDistributor(domain, power_domain)(fp)
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def create_power_operator(domain, power_spectrum, space=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
    ----------
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    domain : Domain, tuple of Domain or DomainTuple
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        Domain over which the power operator shall live.
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    power_spectrum : callable or Field
        An object that contains the power spectrum as a function of k.
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    space : int
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        the domain index on which the power operator will work
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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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    domain = DomainTuple.make(domain)
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    space = utilities.infer_space(domain, space)
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    field = _create_power_field(domain[space], power_spectrum)
    return DiagonalOperator(field, domain, space)
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def create_harmonic_smoothing_operator(domain, space, sigma):
    kfunc = domain[space].get_fft_smoothing_kernel_function(sigma)
    return DiagonalOperator(kfunc(domain[space].get_k_length_array()), domain,
                            space)