power_space.py 9.03 KB
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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 .structured_domain import StructuredDomain
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from .. import dobj
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class PowerSpace(StructuredDomain):
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    """NIFTy class for spaces of power spectra.
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    A power space is the result of a projection of a harmonic domain where
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    k-modes of equal length get mapped to one power index.

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    Parameters
    ----------
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    harmonic_partner : StructuredDomain
        The harmonic dmain of which this is the power space.
    binbounds : None, or tuple of float
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        if None:
            There will be as many bins as there are distinct k-vector lengths
            in the harmonic partner space.
            The "binbounds" property of the PowerSpace will also be None.
        else:
            the bin bounds requested for this PowerSpace. The array
            must be sorted and strictly ascending. The first entry is the right
            boundary of the first bin, and the last entry is the left boundary
            of the last bin, i.e. thee will be len(binbounds)+1 bins in total,
            with the first and last bins reaching to -+infinity, respectively.
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            (default : None)
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    """
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    _powerIndexCache = {}

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    @staticmethod
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    def linear_binbounds(nbin, first_bound, last_bound):
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        """Produces linearly spaced bin bounds.

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        This will produce a binbounds array with nbin-1 entries with
        binbounds[0]=first_bound and binbounds[-1]=last_bound and the remaining
        values equidistantly spaced (in linear scale) between these two.

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        nbin : int
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            the number of bins
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        first_bound, last_bound : float
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            the k values for the right boundary of the first bin and the left
            boundary of the last bin, respectively. They are given in length
            units of the harmonic partner space.
        """
        nbin = int(nbin)
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        if nbin < 3:
            raise ValueError("nbin must be at least 3")
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        return np.linspace(float(first_bound), float(last_bound), nbin-1)
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    @staticmethod
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    def logarithmic_binbounds(nbin, first_bound, last_bound):
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        """Produces logarithmically spaced bin bounds.

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        This will produce a binbounds array with nbin-1 entries with
        binbounds[0]=first_bound and binbounds[-1]=last_bound and the remaining
        values equidistantly spaced (in natural logarithmic scale)
        between these two.

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        nbin : int
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            the number of bins
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        first_bound, last_bound : float
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            the k values for the right boundary of the first bin and the left
            boundary of the last bin, respectively. They are given in length
            units of the harmonic partner space.
        """
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        nbin = int(nbin)
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        if nbin < 3:
            raise ValueError("nbin must be at least 3")
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        return np.logspace(np.log(float(first_bound)),
                           np.log(float(last_bound)),
                           nbin-1, base=np.e)
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    @staticmethod
    def useful_binbounds(space, logarithmic, nbin=None):
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        """Produces bin bounds suitable for a given domain.

        This will produce a binbounds array with `nbin-1` entries, if `nbin` is
        supplied, or the maximum number of entries that does not produce empty
        bins, if `nbin` is not supplied.
        The first and last bin boundary are inferred from `space`.

        space : StructuredDomain
            the domain for which the binbounds will be computed.
        logarithmic : bool
            If True bins will have equal size in linear space; otherwise they
            will have equali size in logarithmic space.
        nbin : int, optional
            the number of bins
            If None, the highest possible number of bins will be used
        """
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        if not (isinstance(space, StructuredDomain) and space.harmonic):
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            raise ValueError("first argument must be a harmonic space.")
        if logarithmic is None and nbin is None:
            return None
        nbin = None if nbin is None else int(nbin)
        logarithmic = bool(logarithmic)
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        dists = space.get_unique_k_lengths()
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        if len(dists) < 3:
            raise ValueError("Space does not have enough unique k lengths")
        lbound = 0.5*(dists[0]+dists[1])
        rbound = 0.5*(dists[-2]+dists[-1])
        dists[0] = lbound
        dists[-1] = rbound
        if logarithmic:
            dists = np.log(dists)
        binsz_min = np.max(np.diff(dists))
        nbin_max = int((dists[-1]-dists[0])/binsz_min)+2
        if nbin is None:
            nbin = nbin_max
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        if nbin < 3:
            raise ValueError("nbin must be at least 3")
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        if nbin > nbin_max:
            raise ValueError("nbin is too large")
        if logarithmic:
            return PowerSpace.logarithmic_binbounds(nbin, lbound, rbound)
        else:
            return PowerSpace.linear_binbounds(nbin, lbound, rbound)

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    def __init__(self, harmonic_partner, binbounds=None):
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        super(PowerSpace, self).__init__()
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        self._needed_for_hash += ['_harmonic_partner', '_binbounds']
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        if not (isinstance(harmonic_partner, StructuredDomain) and
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                harmonic_partner.harmonic):
            raise ValueError("harmonic_partner must be a harmonic space.")
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        if harmonic_partner.scalar_dvol() is None:
            raise ValueError("harmonic partner must have "
                             "scalar volume factors")
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        self._harmonic_partner = harmonic_partner
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        pdvol = harmonic_partner.scalar_dvol()
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        if binbounds is not None:
            binbounds = tuple(binbounds)
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        key = (harmonic_partner, binbounds)
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        if self._powerIndexCache.get(key) is None:
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            k_length_array = self.harmonic_partner.get_k_length_array()
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            if binbounds is None:
                tmp = harmonic_partner.get_unique_k_lengths()
                tbb = 0.5*(tmp[:-1]+tmp[1:])
            else:
                tbb = binbounds
            locdat = np.searchsorted(tbb, dobj.local_data(k_length_array.val))
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            temp_pindex = dobj.from_local_data(
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                k_length_array.val.shape, locdat,
                dobj.distaxis(k_length_array.val))
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            nbin = len(tbb)+1
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            temp_rho = np.bincount(dobj.local_data(temp_pindex).ravel(),
                                   minlength=nbin)
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            temp_rho = dobj.np_allreduce_sum(temp_rho)
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            if (temp_rho == 0).any():
                raise ValueError("empty bins detected")
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            # The explicit conversion to float64 is necessary because bincount
            # sometimes returns its result as an integer array, even when
            # floating-point weights are present ...
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            temp_k_lengths = np.bincount(
                dobj.local_data(temp_pindex).ravel(),
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                weights=dobj.local_data(k_length_array.val).ravel(),
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                minlength=nbin).astype(np.float64, copy=False)
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            temp_k_lengths = dobj.np_allreduce_sum(temp_k_lengths) / temp_rho
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            temp_dvol = temp_rho*pdvol
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            self._powerIndexCache[key] = (binbounds, temp_pindex,
                                          temp_k_lengths, temp_dvol)
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        (self._binbounds, self._pindex, self._k_lengths, self._dvol) = \
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            self._powerIndexCache[key]

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    def __repr__(self):
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        return ("PowerSpace(harmonic_partner=%r, binbounds=%r)"
                % (self.harmonic_partner, self._binbounds))
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    @property
    def harmonic(self):
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        return False
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    @property
    def shape(self):
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        return self.k_lengths.shape
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    @property
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    def size(self):
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        return self.shape[0]

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    def scalar_dvol(self):
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        return None

    def dvol(self):
        return self._dvol
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    @property
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    def harmonic_partner(self):
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        """Returns the Space of which this is the power space."""
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        return self._harmonic_partner
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    @property
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    def binbounds(self):
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        """Returns the boundaries between the power spectrum bins as a tuple.
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        `None` is used to indicate natural binning.
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        """
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        return self._binbounds
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    @property
    def pindex(self):
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        """Returns a data object having the shape of the harmonic partner
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        space containing the indices of the power bin a pixel belongs to.
        """
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        return self._pindex

    @property
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    def k_lengths(self):
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        """Returns a sorted array of all k-modes."""
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        return self._k_lengths