space.py

# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
##
# Copyright (C) 2013 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/>.

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

    .. The NIFTY project homepage is http://www.mpa-garching.mpg.de/ift/nifty/

    NIFTY [#]_, "Numerical Information Field Theory", is a versatile
    library designed to enable the development of signal inference algorithms
    that operate regardless of the underlying spatial grid and its resolution.
    Its object-oriented framework is written in Python, although it accesses
    libraries written in Cython, C++, and C for efficiency.

    NIFTY offers a toolkit that abstracts discretized representations of
    continuous spaces, fields in these spaces, and operators acting on fields
    into classes. Thereby, the correct normalization of operations on fields is
    taken care of automatically without concerning the user. This allows for an
    abstract formulation and programming of inference algorithms, including
    those derived within information field theory. Thus, NIFTY permits its user
    to rapidly prototype algorithms in 1D and then apply the developed code in
    higher-dimensional settings of real world problems. The set of spaces on
    which NIFTY operates comprises point sets, n-dimensional regular grids,
    spherical spaces, their harmonic counterparts, and product spaces
    constructed as combinations of those.

    References
    ----------
    .. [#] Selig et al., "NIFTY -- Numerical Information Field Theory --
        a versatile Python library for signal inference",
        `A&A, vol. 554, id. A26 <http://dx.doi.org/10.1051/0004-6361/201321236>`_,
        2013; `arXiv:1301.4499 <http://www.arxiv.org/abs/1301.4499>`_

    Class & Feature Overview
    ------------------------
    The NIFTY library features three main classes: **spaces** that represent
    certain grids, **fields** that are defined on spaces, and **operators**
    that apply to fields.

    .. Overview of all (core) classes:
    ..
    .. - switch
    .. - notification
    .. - _about
    .. - random
    .. - space
    ..     - point_space
    ..     - rg_space
    ..     - lm_space
    ..     - gl_space
    ..     - hp_space
    ..     - nested_space
    .. - field
    .. - operator
    ..     - diagonal_operator
    ..         - power_operator
    ..     - projection_operator
    ..     - vecvec_operator
    ..     - response_operator
    .. - probing
    ..     - trace_probing
    ..     - diagonal_probing

    Overview of the main classes and functions:

    .. automodule:: nifty

    - :py:class:`space`
        - :py:class:`point_space`
        - :py:class:`rg_space`
        - :py:class:`lm_space`
        - :py:class:`gl_space`
        - :py:class:`hp_space`
        - :py:class:`nested_space`
    - :py:class:`field`
    - :py:class:`operator`
        - :py:class:`diagonal_operator`
            - :py:class:`power_operator`
        - :py:class:`projection_operator`
        - :py:class:`vecvec_operator`
        - :py:class:`response_operator`

        .. currentmodule:: nifty.nifty_tools

        - :py:class:`invertible_operator`
        - :py:class:`propagator_operator`

        .. currentmodule:: nifty.nifty_explicit

        - :py:class:`explicit_operator`

    .. automodule:: nifty

    - :py:class:`probing`
        - :py:class:`trace_probing`
        - :py:class:`diagonal_probing`

        .. currentmodule:: nifty.nifty_explicit

        - :py:class:`explicit_probing`

    .. currentmodule:: nifty.nifty_tools

    - :py:class:`conjugate_gradient`
    - :py:class:`steepest_descent`

    .. currentmodule:: nifty.nifty_explicit

    - :py:func:`explicify`

    .. currentmodule:: nifty.nifty_power

    - :py:func:`weight_power`,
      :py:func:`smooth_power`,
      :py:func:`infer_power`,
      :py:func:`interpolate_power`

"""
from __future__ import division

import abc

import numpy as np
import pylab as pl

from nifty.config import about


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

        NIFTY subclass for unstructured spaces.

        Unstructured spaces are lists of values without any geometrical
        information.

        Parameters
        ----------
        num : int
            Number of points.
        dtype : numpy.dtype, *optional*
            Data type of the field values (default: None).

        Attributes
        ----------
        para : numpy.ndarray
            Array containing the number of points.
        dtype : numpy.dtype
            Data type of the field values.
        discrete : bool
            Parameter captioning the fact that a :py:class:`point_space` is
            always discrete.
        vol : numpy.ndarray
            Pixel volume of the :py:class:`point_space`, which is always 1.
    """

    __metaclass__ = abc.ABCMeta

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

            Parameters
            ----------
            num : int
                Number of points.
            dtype : numpy.dtype, *optional*
                Data type of the field values (default: numpy.float64).

            Returns
            -------
            None.
        """

        # parse dtype
        self.dtype = np.dtype(dtype)

        self._ignore_for_hash = []

    def __hash__(self):
        # Extract the identifying parts from the vars(self) dict.
        result_hash = 0
        for (key, item) in vars(self).items():
            if key in self._ignore_for_hash or key == '_ignore_for_hash':
                continue
            result_hash ^= item.__hash__() ^ int(hash(key)/117)
        return result_hash

    def __eq__(self, x):
        if isinstance(x, type(self)):
            return hash(self) == hash(x)
        else:
            return False

    @abc.abstractproperty
    def harmonic(self):
        raise NotImplementedError

    @abc.abstractproperty
    def shape(self):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic shape for the Space base class."))

    @abc.abstractproperty
    def dim(self):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic dim for the Space base class."))

    @abc.abstractproperty
    def total_volume(self):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic volume for the Space base class."))

    @abc.abstractmethod
    def copy(self):
        return self.__class__(dtype=self.dtype)

    @abc.abstractmethod
    def weight(self, x, power=1, axes=None, inplace=False):
        """
            Weights a given array of field values with the pixel volumes (not
            the meta volumes) to a given power.

            Parameters
            ----------
            x : numpy.ndarray
                Array to be weighted.
            power : float, *optional*
                Power of the pixel volumes to be used (default: 1).

            Returns
            -------
            y : numpy.ndarray
                Weighted array.
        """
        raise NotImplementedError

    def pre_cast(self, x, axes=None):
        return x

    def post_cast(self, x, axes=None):
        return x

    def compute_k_array(self, distribution_strategy):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic k_array for Space base class."))

    def hermitian_decomposition(self, x, axes=None):
        raise NotImplementedError

    def __repr__(self):
        string = ""
        string += str(type(self)) + "\n"
        string += "dtype: " + str(self.dtype) + "\n"
        return string