gl_space.py 5.64 KB
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# NIFTy
# Copyright (C) 2017  Theo Steininger
#
# Author: Theo Steininger
#
# 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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from __future__ import division

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import itertools
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import numpy as np

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from nifty.spaces.space import Space
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from nifty.config import dependency_injector as gdi
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pyHealpix = gdi.get('pyHealpix')


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class GLSpace(Space):
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    """
        ..                 __
        ..               /  /
        ..     ____ __  /  /
        ..   /   _   / /  /
        ..  /  /_/  / /  /_
        ..  \___   /  \___/  space class
        .. /______/

        NIFTY subclass for Gauss-Legendre pixelizations [#]_ of the two-sphere.

        Parameters
        ----------
        nlat : int
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            Number of latitudinal bins (or rings) that are used for this
            pixelization.
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        nlon : int, *optional*
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            Number of longditudinal bins that are used for this pixelization.

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        Attributes
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        ----------
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        dim : np.int
            Total number of dimensionality, i.e. the number of pixels.
        harmonic : bool
            Specifies whether the space is a signal or harmonic space.
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        nlat : int
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            Number of latitudinal bins (or rings) that are used for this
            pixelization.
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        nlon : int
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            Number of longditudinal bins that are used for this pixelization.
        total_volume : np.float
            The total volume of the space.
        shape : tuple of np.ints
            The shape of the space's data array.
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        Raises
        ------
        ValueError
            If input `nlat` or `nlon` is invalid.
        ImportError
            If the pyHealpix module is not available

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

        References
        ----------
        .. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
               harmonic transforms revisited";
               `arXiv:1303.4945 <http://www.arxiv.org/abs/1303.4945>`_
        .. [#] 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.

    """

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    # ---Overwritten properties and methods---

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    def __init__(self, nlat, nlon=None):
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        if 'pyHealpix' not in gdi:
            raise ImportError(
                "The module pyHealpix is needed but not available.")
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        super(GLSpace, self).__init__()
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        self._nlat = self._parse_nlat(nlat)
        self._nlon = self._parse_nlon(nlon)
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    # ---Mandatory properties and methods---
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    @property
    def harmonic(self):
        return False
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    @property
    def shape(self):
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        return (np.int((self.nlat * self.nlon)),)
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    @property
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    def dim(self):
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        return np.int((self.nlat * self.nlon))
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    @property
    def total_volume(self):
        return 4 * np.pi
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    def copy(self):
        return self.__class__(nlat=self.nlat,
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                              nlon=self.nlon)
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    def weight(self, x, power=1, axes=None, inplace=False):
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        nlon = self.nlon
        nlat = self.nlat
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        vol = pyHealpix.GL_weights(nlat, nlon) ** np.float(power)
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        weight = np.array(list(itertools.chain.from_iterable(
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                          itertools.repeat(x, nlon) for x in vol)))
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        if axes is not None:
            # reshape the weight array to match the input shape
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            new_shape = np.ones(len(x.shape), dtype=np.int)
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            # we know len(axes) is always 1
            new_shape[axes[0]] = len(weight)
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            weight = weight.reshape(new_shape)

        if inplace:
            x *= weight
            result_x = x
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        else:
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            result_x = x * weight
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        return result_x
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    def get_distance_array(self, distribution_strategy):
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        raise NotImplementedError
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    def get_fft_smoothing_kernel_function(self, sigma):
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        raise NotImplementedError
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    # ---Added properties and methods---

    @property
    def nlat(self):
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        """ Number of latitudinal bins (or rings) that are used for this
        pixelization.
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        """
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        return self._nlat

    @property
    def nlon(self):
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        """ Number of longditudinal bins that are used for this pixelization.
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        """
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        return self._nlon

    def _parse_nlat(self, nlat):
        nlat = int(nlat)
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        if nlat < 1:
            raise ValueError(
                "nlat must be a positive number.")
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        return nlat

    def _parse_nlon(self, nlon):
        if nlon is None:
            nlon = 2 * self.nlat - 1
        else:
            nlon = int(nlon)
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            if nlon < 1:
                raise ValueError("nlon must be a positive number.")
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        return nlon
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    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
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        hdf5_group['nlat'] = self.nlat
        hdf5_group['nlon'] = self.nlon

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        return None

    @classmethod
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    def _from_hdf5(cls, hdf5_group, repository):
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        result = cls(
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            nlat=hdf5_group['nlat'][()],
            nlon=hdf5_group['nlon'][()],
            )

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        return result