power_space.py

# 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/>.
#
# 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 .space import Space
from .. import dobj


class PowerSpace(Space):
    """NIFTY class for spaces of power spectra.

    Parameters
    ----------
    harmonic_partner : Space
        The harmonic Space of which this is the power space.
    binbounds: None, or tuple/array/list of float
        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.
        (default : None)

    Notes
    -----
    A power space is the result of a projection of a harmonic space where
    k-modes of equal length get mapped to one power index.
    """

    _powerIndexCache = {}

    # ---Overwritten properties and methods---

    @staticmethod
    def linear_binbounds(nbin, first_bound, last_bound):
        """
        nbin: integer
            the number of bins
        first_bound, last_bound: float
            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.
        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.
        """
        nbin = int(nbin)
        assert nbin >= 3, "nbin must be at least 3"
        return np.linspace(float(first_bound), float(last_bound), nbin-1)

    @staticmethod
    def logarithmic_binbounds(nbin, first_bound, last_bound):
        """
        nbin: integer
            the number of bins
        first_bound, last_bound: float
            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.
        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.
        """
        nbin = int(nbin)
        assert nbin >= 3, "nbin must be at least 3"
        return np.logspace(np.log(float(first_bound)),
                           np.log(float(last_bound)),
                           nbin-1, base=np.e)

    @staticmethod
    def useful_binbounds(space, logarithmic, nbin=None):
        if not (isinstance(space, Space) and space.harmonic):
            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)
        dists = space.get_unique_k_lengths()
        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
        assert nbin >= 3, "nbin must be at least 3"
        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)

    def __init__(self, harmonic_partner, binbounds=None):
        super(PowerSpace, self).__init__()
        self._needed_for_hash += ['_harmonic_partner', '_binbounds']

        if not (isinstance(harmonic_partner, Space) and
                harmonic_partner.harmonic):
            raise ValueError("harmonic_partner must be a harmonic space.")
        if harmonic_partner.scalar_dvol() is None:
            raise ValueError("harmonic partner must have "
                             "scalar volume factors")
        self._harmonic_partner = harmonic_partner
        pdvol = harmonic_partner.scalar_dvol()

        if binbounds is not None:
            binbounds = tuple(binbounds)

        key = (harmonic_partner, binbounds)
        if self._powerIndexCache.get(key) is None:
            k_length_array = self.harmonic_partner.get_k_length_array()
            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))
            temp_pindex = dobj.from_local_data(
                k_length_array.val.shape, locdat, dobj.distaxis(k_length_array.val))
            nbin = len(tbb)+1
            temp_rho = np.bincount(dobj.local_data(temp_pindex).ravel(),
                                   minlength=nbin)
            temp_rho = dobj.np_allreduce_sum(temp_rho)
            assert not (temp_rho == 0).any(), "empty bins detected"
            # The explicit conversion to float64 is necessary because bincount
            # sometimes returns its result as an integer array, even when
            # floating-point weights are present ...
            temp_k_lengths = np.bincount(dobj.local_data(temp_pindex).ravel(),
                weights=dobj.local_data(k_length_array.val).ravel(),
                minlength=nbin).astype(np.float64)
            temp_k_lengths = dobj.np_allreduce_sum(temp_k_lengths) / temp_rho
            temp_dvol = temp_rho*pdvol
            self._powerIndexCache[key] = (binbounds,
                                          temp_pindex,
                                          temp_k_lengths,
                                          temp_dvol)

        (self._binbounds, self._pindex, self._k_lengths, self._dvol) = \
            self._powerIndexCache[key]

    # ---Mandatory properties and methods---

    def __repr__(self):
        return ("PowerSpace(harmonic_partner=%r, binbounds=%r)"
                % (self.harmonic_partner, self._binbounds))

    @property
    def harmonic(self):
        return False

    @property
    def shape(self):
        return self.k_lengths.shape

    @property
    def dim(self):
        return self.shape[0]

    def scalar_dvol(self):
        return None

    def dvol(self):
        return self._dvol

    # ---Added properties and methods---

    @property
    def harmonic_partner(self):
        """Returns the Space of which this is the power space."""
        return self._harmonic_partner

    @property
    def binbounds(self):
        """Returns the boundaries between the power spectrum bins as a tuple.
        None is used to indicate natural binning.
        """
        return self._binbounds

    @property
    def pindex(self):
        """Returns a data object having the shape of the harmonic partner
        space containing the indices of the power bin a pixel belongs to.
        """
        return self._pindex

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