hp_space.py 5.99 KB
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# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
#
# Copyright (C) 2015 Max-Planck-Society
#
# Author: Marco Selig
# Project homepage: <http://www.mpa-garching.mpg.de/ift/nifty/>
#
# 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/>.

"""
    ..                  __   ____   __
    ..                /__/ /   _/ /  /_
    ..      __ ___    __  /  /_  /   _/  __   __
    ..    /   _   | /  / /   _/ /  /   /  / /  /
    ..   /  / /  / /  / /  /   /  /_  /  /_/  /
    ..  /__/ /__/ /__/ /__/    \___/  \___   /  lm
    ..                               /______/

    NIFTY submodule for grids on the two-sphere.

"""
from __future__ import division

import numpy as np
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from d2o import arange, STRATEGIES as DISTRIBUTION_STRATEGIES
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from nifty.config import about
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from nifty.spaces.space import Space
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from nifty.config import nifty_configuration as gc, \
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                         dependency_injector as gdi

hp = gdi.get('healpy')

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class HPSpace(Space):
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    """
        ..        __
        ..      /  /
        ..     /  /___    ______
        ..    /   _   | /   _   |
        ..   /  / /  / /  /_/  /
        ..  /__/ /__/ /   ____/  space class
        ..           /__/

        NIFTY subclass for HEALPix discretizations of the two-sphere [#]_.

        Parameters
        ----------
        nside : int
            Resolution parameter for the HEALPix discretization, resulting in
            ``12*nside**2`` pixels.

        See Also
        --------
        gl_space : A class for the Gauss-Legendre discretization of the
            sphere [#]_.
        lm_space : A class for spherical harmonic components.

        Notes
        -----
        Only powers of two are allowed for `nside`.

        References
        ----------
        .. [#] K.M. Gorski et al., 2005, "HEALPix: A Framework for
               High-Resolution Discretization and Fast Analysis of Data
               Distributed on the Sphere", *ApJ* 622..759G.
        .. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
               harmonic transforms revisited";
               `arXiv:1303.4945 <http://www.arxiv.org/abs/1303.4945>`_

        Attributes
        ----------
        para : numpy.ndarray
            Array containing the number `nside`.
        dtype : numpy.dtype
            Data type of the field values, which is always numpy.float64.
        discrete : bool
            Whether or not the underlying space is discrete, always ``False``
            for spherical spaces.
        vol : numpy.ndarray
            An array with one element containing the pixel size.
    """

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    # ---Overwritten properties and methods---

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    def __init__(self, nside=2, dtype=np.dtype('float')):
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        """
            Sets the attributes for a hp_space class instance.

            Parameters
            ----------
            nside : int
                Resolution parameter for the HEALPix discretization, resulting
                in ``12*nside**2`` pixels.

            Returns
            -------
            None

            Raises
            ------
            ImportError
                If the healpy module is not available.
            ValueError
                If input `nside` is invaild.

        """
        # check imports
        if not gc['use_healpy']:
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            raise ImportError("ERROR: healpy not available or not loaded.")
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        super(HPSpace, self).__init__(dtype)
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        self._nside = self._parse_nside(nside)
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    def distance_array(self, distribution_strategy):
        """
        Calculates distance from center to all the points on the sphere

        Parameters
        ----------
        distribution_strategy: Result d2o's distribution strategy

        Returns
        -------
        dists: distributed_data_object
        """
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        dists = arange(
            start=0, stop = self.shape[0], dtype=np.float128,
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            distribution_strategy=distribution_strategy
        )

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        # setting the center to fixed value
        center_vec = (1, 0, 0)
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        dists = dists.apply_scalar_function(
            lambda x: np.arccos(np.dot(hp.pix2vec(self.nside, int(x)),
                                       center_vec))
        )
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        return dists

    def codomain_smoothing_function(self, sigma, target):
        if sigma is None:
            sigma = np.sqrt(2) * np.pi / (target.lmax + 1)

        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma**2)

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    # ---Mandatory properties and methods---

    @property
    def harmonic(self):
        return False
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    @property
    def shape(self):
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        return (np.int(12 * self.nside ** 2),)
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    @property
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    def dim(self):
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        return np.int(12 * self.nside ** 2)
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    @property
    def total_volume(self):
        return 4 * np.pi
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    def copy(self):
        return self.__class__(nside=self.nside,
                              dtype=self.dtype)

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    def weight(self, x, power=1, axes=None, inplace=False):
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        weight = ((4*np.pi) / (12 * self.nside**2)) ** power
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        if inplace:
            x *= weight
            result_x = x
        else:
            result_x = x * weight

        return result_x
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    # ---Added properties and methods---

    @property
    def nside(self):
        return self._nside

    def _parse_nside(self, nside):
        nside = int(nside)
        if nside & (nside - 1) != 0 or nside < 2:
            raise ValueError(about._errors.cstring(
                "ERROR: nside must be positive and a multiple of 2."))
        return nside