power_space.py 9.67 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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import numpy as np

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import d2o

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from power_index_factory import PowerIndexFactory

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from nifty.spaces.space import Space
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class PowerSpace(Space):
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    """ NIFTY class for spaces of power spectra.

    Parameters
    ----------
    harmonic_partner : Space
        The harmonic Space of which this is the power space.
    distribution_strategy : str *optional*
        The distribution strategy used for the distributed_data_objects
        derived from this PowerSpace, e.g. the pindex.
        (default : 'not')
    logarithmic : bool *optional*
        True if logarithmic binning should be used (default : False).
    nbin : {int, None} *optional*
        The number of bins that should be used for power spectrum binning
        (default : None).
        if nbin == None, then nbin is set to the length of kindex.
    binbounds :  {list, array-like} *optional*
        Array-like inner boundaries of the used bins of the default
        indices.
        (default : None)
        if binbounds == None :
            Calculates the bounds from the kindex while applying the
            logarithmic and nbin keywords.

    Attributes
    ----------
    pindex : distributed_data_object
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        This holds the information which pixel of the harmonic partner gets
        mapped to which power bin
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    kindex : numpy.ndarray
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        Sorted array of all k-modes.
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    pundex : numpy.ndarray
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        Flat index of the first occurence of a k-vector with length==kindex[n]
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        in the k_array.
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    rho : numpy.ndarray
        The amount of k-modes that get mapped to one power bin is given by
        rho.
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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.
    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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    config : {logarithmic, nbin, binbounds}
        Dictionary storing the values for `logarithmic`, `nbin`, and
        `binbounds` that were used during initialization.
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    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.

    """
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    # ---Overwritten properties and methods---

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    def __init__(self, harmonic_partner,
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                 distribution_strategy='not',
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                 logarithmic=False, nbin=None, binbounds=None):
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        super(PowerSpace, self).__init__()
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        self._ignore_for_hash += ['_pindex', '_kindex', '_rho', '_pundex',
                                  '_k_array']
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        if not isinstance(harmonic_partner, Space):
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            raise ValueError(
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                "harmonic_partner must be a Space.")
        if not harmonic_partner.harmonic:
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            raise ValueError(
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                "harmonic_partner must be a harmonic space.")
        self._harmonic_partner = harmonic_partner
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        power_index = PowerIndexFactory.get_power_index(
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                        domain=self.harmonic_partner,
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                        distribution_strategy=distribution_strategy,
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                        logarithmic=logarithmic,
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                        nbin=nbin,
                        binbounds=binbounds)
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        self._config = power_index['config']
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        self._pindex = power_index['pindex']
        self._kindex = power_index['kindex']
        self._rho = power_index['rho']
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        self._pundex = power_index['pundex']
        self._k_array = power_index['k_array']
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    def pre_cast(self, x, axes):
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        """ Casts power spectrum functions to discretized power spectra.

        This function takes an array or a function. If it is an array it does
        nothing, otherwise it interpretes the function as power spectrum and
        evaluates it at every k-mode.

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        Parameters
        ----------
        x : {array-like, function array-like -> array-like}
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            power spectrum given either in discretized form or implicitly as a
            function
        axes : tuple of ints
            Specifies the axes of x which correspond to this space. For
            explicifying the power spectrum function, this is ignored.

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        Returns
        -------
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        array-like
            discretized power spectrum

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        """
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        if callable(x):
            return x(self.kindex)
        else:
            return x

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    # ---Mandatory properties and methods---

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

    @property
    def total_volume(self):
        # every power-pixel has a volume of 1
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        return float(reduce(lambda x, y: x*y, self.pindex.shape))
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    def copy(self):
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        distribution_strategy = self.pindex.distribution_strategy
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        return self.__class__(harmonic_partner=self.harmonic_partner,
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                              distribution_strategy=distribution_strategy,
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                              logarithmic=self.config["logarithmic"],
                              nbin=self.config["nbin"],
                              binbounds=self.config["binbounds"])
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    def weight(self, x, power=1, axes=None, inplace=False):
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        reshaper = [1, ] * len(x.shape)
        # we know len(axes) is always 1
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        reshaper[axes[0]] = self.shape[0]

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        weight = self.rho.reshape(reshaper)
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        if power != 1:
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            weight = weight ** np.float(power)
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        if inplace:
            x *= weight
            result_x = x
        else:
            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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        result = d2o.distributed_data_object(
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                                self.kindex, dtype=np.float64,
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                                distribution_strategy=distribution_strategy)
        return result
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    def get_fft_smoothing_kernel_function(self, sigma):
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        raise NotImplementedError(
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            "There is no fft smoothing function for PowerSpace.")
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    # ---Added properties and methods---

    @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 config(self):
        """ Returns the configuration which was used for `logarithmic`, `nbin`
        and `binbounds` during initialization.
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        """
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        return self._config
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    @property
    def pindex(self):
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        """ A distributed_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
    def kindex(self):
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        """ Sorted array of all k-modes.
        """
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        return self._kindex

    @property
    def rho(self):
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        """Degeneracy factor of the individual k-vectors.
        """
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        return self._rho
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    @property
    def pundex(self):
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        """ An array for which the n-th entry gives the flat index of the
        first occurence of a k-vector with length==kindex[n] in the
        k_array.
        """
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        return self._pundex

    @property
    def k_array(self):
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        """ An array containing distances to the grid center (i.e. zero-mode)
        for every k-mode in the grid of the harmonic partner space.
        """
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        return self._k_array
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    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
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        hdf5_group['kindex'] = self.kindex
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        hdf5_group['rho'] = self.rho
        hdf5_group['pundex'] = self.pundex
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        hdf5_group['logarithmic'] = self.config["logarithmic"]
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        # Store nbin as string, since it can be None
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        hdf5_group.attrs['nbin'] = str(self.config["nbin"])
        hdf5_group.attrs['binbounds'] = str(self.config["binbounds"])
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        return {
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            'harmonic_partner': self.harmonic_partner,
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            'pindex': self.pindex,
            'k_array': self.k_array
        }

    @classmethod
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    def _from_hdf5(cls, hdf5_group, repository):
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        # make an empty PowerSpace object
        new_ps = EmptyPowerSpace()
        # reset class
        new_ps.__class__ = cls
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        # call instructor so that classes are properly setup
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        super(PowerSpace, new_ps).__init__()
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        # set all values
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        new_ps._harmonic_partner = repository.get('harmonic_partner',
                                                  hdf5_group)
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        new_ps._config = {}
        new_ps._config['logarithmic'] = hdf5_group['logarithmic'][()]
        exec("new_ps._config['nbin'] = " + hdf5_group.attrs['nbin'])
        exec("new_ps._config['binbounds'] = " + hdf5_group.attrs['binbounds'])
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        new_ps._pindex = repository.get('pindex', hdf5_group)
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        new_ps._kindex = hdf5_group['kindex'][:]
        new_ps._rho = hdf5_group['rho'][:]
        new_ps._pundex = hdf5_group['pundex'][:]
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        new_ps._k_array = repository.get('k_array', hdf5_group)
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        new_ps._ignore_for_hash += ['_pindex', '_kindex', '_rho', '_pundex',
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                                    '_k_array']
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        return new_ps


class EmptyPowerSpace(PowerSpace):
    def __init__(self):
        pass