space.py 8.93 KB
Newer Older
1 2
# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
Marco Selig's avatar
Marco Selig committed
3
##
4
# Copyright (C) 2013 Max-Planck-Society
Marco Selig's avatar
Marco Selig committed
5
##
6 7
# Author: Marco Selig
# Project homepage: <http://www.mpa-garching.mpg.de/ift/nifty/>
Marco Selig's avatar
Marco Selig committed
8
##
9 10 11 12
# 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.
Marco Selig's avatar
Marco Selig committed
13
##
14 15 16 17
# 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.
Marco Selig's avatar
Marco Selig committed
18
##
19 20
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
Marco Selig's avatar
Marco Selig committed
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

"""
    ..                  __   ____   __
    ..                /__/ /   _/ /  /_
    ..      __ ___    __  /  /_  /   _/  __   __
    ..    /   _   | /  / /   _/ /  /   /  / /  /
    ..   /  / /  / /  / /  /   /  /_  /  /_/  /
    ..  /__/ /__/ /__/ /__/    \___/  \___   /  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
Marco Selig's avatar
Marco Selig committed
45
    to rapidly prototype algorithms in 1D and then apply the developed code in
Marco Selig's avatar
Marco Selig committed
46 47 48 49 50
    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.

51 52 53 54 55 56 57
    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>`_

Marco Selig's avatar
Marco Selig committed
58 59 60 61 62 63
    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.

64 65
    .. Overview of all (core) classes:
    ..
Marco Selig's avatar
Marco Selig committed
66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87
    .. - 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

88 89
    Overview of the main classes and functions:

Marco Selig's avatar
Marco Selig committed
90 91
    .. automodule:: nifty

92 93 94 95 96 97 98 99 100 101 102 103 104 105
    - :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`
Marco Selig's avatar
Marco Selig committed
106

107
        .. currentmodule:: nifty.nifty_tools
Marco Selig's avatar
Marco Selig committed
108

109 110
        - :py:class:`invertible_operator`
        - :py:class:`propagator_operator`
Marco Selig's avatar
Marco Selig committed
111

112
        .. currentmodule:: nifty.nifty_explicit
Marco Selig's avatar
Marco Selig committed
113

114
        - :py:class:`explicit_operator`
Marco Selig's avatar
Marco Selig committed
115

116
    .. automodule:: nifty
Marco Selig's avatar
Marco Selig committed
117

118 119 120
    - :py:class:`probing`
        - :py:class:`trace_probing`
        - :py:class:`diagonal_probing`
Marco Selig's avatar
Marco Selig committed
121

122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
        .. 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`
Marco Selig's avatar
Marco Selig committed
141 142 143

"""
from __future__ import division
144 145 146

import abc

Marco Selig's avatar
Marco Selig committed
147 148
import numpy as np

Ultimanet's avatar
Ultimanet committed
149

theos's avatar
theos committed
150
class Space(object):
Marco Selig's avatar
Marco Selig committed
151
    """
Ultimanet's avatar
Ultimanet committed
152 153 154 155 156 157 158
        ..                            __             __
        ..                          /__/           /  /_
        ..      ______    ______    __   __ ___   /   _/
        ..    /   _   | /   _   | /  / /   _   | /  /
        ..   /  /_/  / /  /_/  / /  / /  / /  / /  /_
        ..  /   ____/  \______/ /__/ /__/ /__/  \___/  space class
        .. /__/
Marco Selig's avatar
Marco Selig committed
159

Ultimanet's avatar
Ultimanet committed
160
        NIFTY subclass for unstructured spaces.
Marco Selig's avatar
Marco Selig committed
161

Ultimanet's avatar
Ultimanet committed
162 163
        Unstructured spaces are lists of values without any geometrical
        information.
Marco Selig's avatar
Marco Selig committed
164 165 166

        Parameters
        ----------
Ultimanet's avatar
Ultimanet committed
167 168
        num : int
            Number of points.
169
        dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
170
            Data type of the field values (default: None).
Marco Selig's avatar
Marco Selig committed
171

Ultimanet's avatar
Ultimanet committed
172
        Attributes
Marco Selig's avatar
Marco Selig committed
173
        ----------
Ultimanet's avatar
Ultimanet committed
174 175
        para : numpy.ndarray
            Array containing the number of points.
176
        dtype : numpy.dtype
Ultimanet's avatar
Ultimanet committed
177 178 179 180 181 182
            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.
Marco Selig's avatar
Marco Selig committed
183
    """
184

185 186 187
    __metaclass__ = abc.ABCMeta

    def __init__(self, dtype=np.dtype('float')):
Ultimanet's avatar
Ultimanet committed
188 189
        """
            Sets the attributes for a point_space class instance.
Marco Selig's avatar
Marco Selig committed
190

Ultimanet's avatar
Ultimanet committed
191 192 193 194
            Parameters
            ----------
            num : int
                Number of points.
195
            dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
196
                Data type of the field values (default: numpy.float64).
Marco Selig's avatar
Marco Selig committed
197

Ultimanet's avatar
Ultimanet committed
198 199 200 201
            Returns
            -------
            None.
        """
202

203
        # parse dtype
204
        self.dtype = np.dtype(dtype)
205

206
        self._ignore_for_hash = []
207

Ultima's avatar
Ultima committed
208 209 210 211
    def __hash__(self):
        # Extract the identifying parts from the vars(self) dict.
        result_hash = 0
        for (key, item) in vars(self).items():
212
            if key in self._ignore_for_hash or key == '_ignore_for_hash':
Ultima's avatar
Ultima committed
213
                continue
theos's avatar
theos committed
214
            result_hash ^= item.__hash__() ^ int(hash(key)/117)
Ultima's avatar
Ultima committed
215 216
        return result_hash

theos's avatar
theos committed
217 218 219 220 221
    def __eq__(self, x):
        if isinstance(x, type(self)):
            return hash(self) == hash(x)
        else:
            return False
222

theos's avatar
theos committed
223 224 225
    def __ne__(self, x):
        return not self.__eq__(x)

226 227 228
    @abc.abstractproperty
    def harmonic(self):
        raise NotImplementedError
229

230
    @abc.abstractproperty
231
    def shape(self):
232 233
        raise NotImplementedError(
            "There is no generic shape for the Space base class.")
Marco Selig's avatar
Marco Selig committed
234

235
    @abc.abstractproperty
236
    def dim(self):
237 238
        raise NotImplementedError(
            "There is no generic dim for the Space base class.")
Marco Selig's avatar
Marco Selig committed
239

240
    @abc.abstractproperty
241
    def total_volume(self):
242 243
        raise NotImplementedError(
            "There is no generic volume for the Space base class.")
244

245 246 247
    @abc.abstractmethod
    def copy(self):
        return self.__class__(dtype=self.dtype)
248

249
    @abc.abstractmethod
250
    def weight(self, x, power=1, axes=None, inplace=False):
Marco Selig's avatar
Marco Selig committed
251
        """
Ultimanet's avatar
Ultimanet committed
252 253
            Weights a given array of field values with the pixel volumes (not
            the meta volumes) to a given power.
Marco Selig's avatar
Marco Selig committed
254 255 256

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
257 258 259 260
            x : numpy.ndarray
                Array to be weighted.
            power : float, *optional*
                Power of the pixel volumes to be used (default: 1).
Marco Selig's avatar
Marco Selig committed
261 262

            Returns
Ultimanet's avatar
Ultimanet committed
263 264 265
            -------
            y : numpy.ndarray
                Weighted array.
Marco Selig's avatar
Marco Selig committed
266
        """
267
        raise NotImplementedError
Ultima's avatar
Ultima committed
268

269 270 271 272
    def pre_cast(self, x, axes=None):
        return x

    def post_cast(self, x, axes=None):
273 274
        return x

275
    def get_distance_array(self, distribution_strategy):
276
        raise NotImplementedError(
277 278 279 280 281
            "There is no generic distance structure for Space base class.")

    def get_smoothing_kernel_function(self, sigma):
        raise NotImplementedError(
            "There is no generic co-smoothing kernel for Space base class.")
282

283 284 285
    def hermitian_decomposition(self, x, axes=None):
        raise NotImplementedError

286
    def __repr__(self):
Ultima's avatar
Ultima committed
287 288
        string = ""
        string += str(type(self)) + "\n"
289
        string += "dtype: " + str(self.dtype) + "\n"
Ultima's avatar
Ultima committed
290
        return string