space.py 13.3 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
141 142 143 144

"""
from __future__ import division
import numpy as np
Marco Selig's avatar
Marco Selig committed
145
import pylab as pl
146

csongor's avatar
csongor committed
147
from nifty.config import about
theos's avatar
theos committed
148
from space_paradict import SpaceParadict
Marco Selig's avatar
Marco Selig committed
149

Ultimanet's avatar
Ultimanet committed
150

theos's avatar
theos committed
151
class Space(object):
Marco Selig's avatar
Marco Selig committed
152
    """
Ultimanet's avatar
Ultimanet committed
153 154 155 156 157 158 159
        ..                            __             __
        ..                          /__/           /  /_
        ..      ______    ______    __   __ ___   /   _/
        ..    /   _   | /   _   | /  / /   _   | /  /
        ..   /  /_/  / /  /_/  / /  / /  / /  / /  /_
        ..  /   ____/  \______/ /__/ /__/ /__/  \___/  space class
        .. /__/
Marco Selig's avatar
Marco Selig committed
160

Ultimanet's avatar
Ultimanet committed
161
        NIFTY subclass for unstructured spaces.
Marco Selig's avatar
Marco Selig committed
162

Ultimanet's avatar
Ultimanet committed
163 164
        Unstructured spaces are lists of values without any geometrical
        information.
Marco Selig's avatar
Marco Selig committed
165 166 167

        Parameters
        ----------
Ultimanet's avatar
Ultimanet committed
168 169
        num : int
            Number of points.
170
        dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
171
            Data type of the field values (default: None).
Marco Selig's avatar
Marco Selig committed
172

Ultimanet's avatar
Ultimanet committed
173
        Attributes
Marco Selig's avatar
Marco Selig committed
174
        ----------
Ultimanet's avatar
Ultimanet committed
175 176
        para : numpy.ndarray
            Array containing the number of points.
177
        dtype : numpy.dtype
Ultimanet's avatar
Ultimanet committed
178 179 180 181 182 183
            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
184
    """
185

186
    def __init__(self, dtype=np.dtype('float'), **kwargs):
Ultimanet's avatar
Ultimanet committed
187 188
        """
            Sets the attributes for a point_space class instance.
Marco Selig's avatar
Marco Selig committed
189

Ultimanet's avatar
Ultimanet committed
190 191 192 193
            Parameters
            ----------
            num : int
                Number of points.
194
            dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
195
                Data type of the field values (default: numpy.float64).
Marco Selig's avatar
Marco Selig committed
196

Ultimanet's avatar
Ultimanet committed
197 198 199 200
            Returns
            -------
            None.
        """
theos's avatar
theos committed
201
        self.paradict = SpaceParadict(**kwargs)
202

203 204
        # parse dtype
        dtype = np.dtype(dtype)
Ultima's avatar
Ultima committed
205
        self.dtype = dtype
theos's avatar
theos committed
206
        self._harmonic = None
207

theos's avatar
theos committed
208 209 210
    @property
    def harmonic(self):
        return self._harmonic
211

Ultima's avatar
Ultima committed
212 213 214 215
    def __hash__(self):
        # Extract the identifying parts from the vars(self) dict.
        result_hash = 0
        for (key, item) in vars(self).items():
216
            if key in []:
Ultima's avatar
Ultima committed
217
                continue
theos's avatar
theos committed
218
            result_hash ^= item.__hash__() ^ int(hash(key)/117)
Ultima's avatar
Ultima committed
219 220
        return result_hash

theos's avatar
theos committed
221 222 223 224 225
    def __eq__(self, x):
        if isinstance(x, type(self)):
            return hash(self) == hash(x)
        else:
            return False
226

227
    def copy(self):
theos's avatar
theos committed
228
        return self.__class__(dtype=self.dtype, **self.paradict.parameters)
229

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

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

240
    @property
241
    def total_volume(self):
theos's avatar
theos committed
242 243
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic volume for the Space base class."))
244

245
    def complement_cast(self, x, axes=None):
246 247
        return x

248
    def weight(self, x, power=1, axes=None, inplace=False):
Marco Selig's avatar
Marco Selig committed
249
        """
Ultimanet's avatar
Ultimanet committed
250 251
            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
252 253 254

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
255 256 257 258
            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
259 260

            Returns
Ultimanet's avatar
Ultimanet committed
261 262 263
            -------
            y : numpy.ndarray
                Weighted array.
Marco Selig's avatar
Marco Selig committed
264
        """
265
        raise NotImplementedError
Ultima's avatar
Ultima committed
266

267 268 269
    def compute_k_array(self, distribution_strategy):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic k_array for Space base class."))
270

271 272
    def get_plot(self, x, title="", vmin=None, vmax=None, unit=None,
                 norm=None, other=None, legend=False, save=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
273
        """
274 275
            Creates a plot of field values according to the specifications
            given by the parameters.
Marco Selig's avatar
Marco Selig committed
276 277 278

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
279
            x : numpy.ndarray
280
                Array containing the field values.
Marco Selig's avatar
Marco Selig committed
281 282 283

            Returns
            -------
284
            None
285

Ultimanet's avatar
Ultimanet committed
286
            Other parameters
287
            ----------------
288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
            title : string, *optional*
                Title of the plot (default: "").
            vmin : float, *optional*
                Minimum value to be displayed (default: ``min(x)``).
            vmax : float, *optional*
                Maximum value to be displayed (default: ``max(x)``).
            unit : string, *optional*
                Unit of the field values (default: "").
            norm : string, *optional*
                Scaling of the field values before plotting (default: None).
            other : {single object, tuple of objects}, *optional*
                Object or tuple of objects to be added, where objects can be
                scalars, arrays, or fields (default: None).
            legend : bool, *optional*
                Whether to show the legend or not (default: False).
            save : string, *optional*
                Valid file name where the figure is to be stored, by default
                the figure is not saved (default: False).

Ultimanet's avatar
Ultimanet committed
307
        """
308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323
        if not pl.isinteractive() and save is not None:
            about.warnings.cprint("WARNING: interactive mode off.")

        x = self.cast(x)

        fig = pl.figure(num=None,
                        figsize=(6.4, 4.8),
                        dpi=None,
                        facecolor="none",
                        edgecolor="none",
                        frameon=False,
                        FigureClass=pl.Figure)

        ax0 = fig.add_axes([0.12, 0.12, 0.82, 0.76])
        xaxes = np.arange(self.para[0], dtype=np.dtype('int'))

324
        if (norm == "log") and (vmin <= 0):
325 326 327 328 329 330 331 332
            raise ValueError(about._errors.cstring(
                "ERROR: nonpositive value(s)."))

        if issubclass(self.dtype.type, np.complexfloating):
            if vmin is None:
                vmin = min(x.real.min(), x.imag.min(), abs(x).min())
            if vmax is None:
                vmax = min(x.real.max(), x.imag.max(), abs(x).max())
Ultimanet's avatar
Ultimanet committed
333
        else:
334 335 336 337
            if vmin is None:
                vmin = x.min()
            if vmax is None:
                vmax = x.max()
Ultimanet's avatar
Ultimanet committed
338

339 340 341
        ax0.set_xlim(xaxes[0], xaxes[-1])
        ax0.set_xlabel("index")
        ax0.set_ylim(vmin, vmax)
342

343 344
        if(norm == "log"):
            ax0.set_yscale('log')
Marco Selig's avatar
Marco Selig committed
345

346 347 348 349 350 351 352 353 354 355 356 357 358 359
        if issubclass(self.dtype.type, np.complexfloating):
            ax0.scatter(xaxes, self.unary_operation(x, op='abs'),
                        color=[0.0, 0.5, 0.0], marker='o',
                        label="graph (absolute)", facecolor="none", zorder=1)
            ax0.scatter(xaxes, self.unary_operation(x, op='real'),
                        color=[0.0, 0.5, 0.0], marker='s',
                        label="graph (real part)", facecolor="none", zorder=1)
            ax0.scatter(xaxes, self.unary_operation(x, op='imag'),
                        color=[0.0, 0.5, 0.0], marker='D',
                        label="graph (imaginary part)", facecolor="none",
                        zorder=1)
        else:
            ax0.scatter(xaxes, x, color=[0.0, 0.5, 0.0], marker='o',
                        label="graph 0", zorder=1)
Marco Selig's avatar
Marco Selig committed
360

361 362 363 364 365 366 367 368 369 370 371 372
        if other is not None:
            if not isinstance(other, tuple):
                other = (other, )
            imax = max(1, len(other) - 1)
            for ii in xrange(len(other)):
                ax0.scatter(xaxes, self.dtype(other[ii]),
                            color=[max(0.0, 1.0 - (2 * ii / imax)**2),
                                   0.5 * ((2 * ii - imax) / imax)**2,
                                   max(0.0, 1.0 -
                                       (2 * (ii - imax) / imax)**2)],
                            marker='o', label="'other' graph " + str(ii),
                            zorder=-ii)
Ultimanet's avatar
Ultimanet committed
373

374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390
        if legend:
            ax0.legend()

        if unit is not None:
            unit = " [" + unit + "]"
        else:
            unit = ""

        ax0.set_ylabel("values" + unit)
        ax0.set_title(title)

        if save is not None:
            fig.savefig(str(save), dpi=None,
                        facecolor="none", edgecolor="none")
            pl.close(fig)
        else:
            fig.canvas.draw()
Marco Selig's avatar
Marco Selig committed
391

392
    def __repr__(self):
Ultima's avatar
Ultima committed
393 394
        string = ""
        string += str(type(self)) + "\n"
Ultima's avatar
Ultima committed
395
        string += "paradict: " + str(self.paradict) + "\n"
396 397
        string += "dtype: " + str(self.dtype) + "\n"
        string += "harmonic: " + str(self.harmonic) + "\n"
Ultima's avatar
Ultima committed
398
        return string