nifty_core.py 115 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

147
from nifty_paradict import space_paradict,\
148
    point_space_paradict
Ultimanet's avatar
Ultimanet committed
149

150
from keepers import about,\
151
152
153
    global_configuration as gc,\
    global_dependency_injector as gdi

Ultimanet's avatar
Ultimanet committed
154
from nifty_random import random
155
from nifty.nifty_mpi_data import distributed_data_object,\
156
    STRATEGIES as DISTRIBUTION_STRATEGIES
157

158
import nifty.nifty_utilities as utilities
Marco Selig's avatar
Marco Selig committed
159

160
POINT_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']
Marco Selig's avatar
Marco Selig committed
161

Ultimanet's avatar
Ultimanet committed
162
163

class space(object):
Marco Selig's avatar
Marco Selig committed
164
    """
Ultimanet's avatar
Ultimanet committed
165
166
167
168
169
170
171
        ..     _______   ______    ____ __   _______   _______
        ..   /  _____/ /   _   | /   _   / /   ____/ /   __  /
        ..  /_____  / /  /_/  / /  /_/  / /  /____  /  /____/
        .. /_______/ /   ____/  \______|  \______/  \______/  class
        ..          /__/

        NIFTY base class for spaces and their discretizations.
Marco Selig's avatar
Marco Selig committed
172

Ultimanet's avatar
Ultimanet committed
173
174
175
        The base NIFTY space class is an abstract class from which other
        specific space subclasses, including those preimplemented in NIFTY
        (e.g. the regular grid class) must be derived.
Marco Selig's avatar
Marco Selig committed
176
177
178

        Parameters
        ----------
179
        dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
180
181
            Data type of the field values for a field defined on this space
            (default: numpy.float64).
182
        datamodel :
Marco Selig's avatar
Marco Selig committed
183
184
185

        See Also
        --------
Ultimanet's avatar
Ultimanet committed
186
187
188
189
190
191
192
193
        point_space :  A class for unstructured lists of numbers.
        rg_space : A class for regular cartesian grids in arbitrary dimensions.
        hp_space : A class for the HEALPix discretization of the sphere
            [#]_.
        gl_space : A class for the Gauss-Legendre discretization of the sphere
            [#]_.
        lm_space : A class for spherical harmonic components.
        nested_space : A class for product spaces.
Marco Selig's avatar
Marco Selig committed
194

Ultimanet's avatar
Ultimanet committed
195
196
197
198
199
200
201
202
        References
        ----------
        .. [#] 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.
        .. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
               harmonic transforms revisited";
               `arXiv:1303.4945 <http://www.arxiv.org/abs/1303.4945>`_
Marco Selig's avatar
Marco Selig committed
203
204
205

        Attributes
        ----------
Ultimanet's avatar
Ultimanet committed
206
        para : {single object, list of objects}
207
208
209
            This is a freeform list of parameters that derivatives of the space
            class can use.
        dtype : numpy.dtype
Ultimanet's avatar
Ultimanet committed
210
211
212
213
214
215
216
            Data type of the field values for a field defined on this space.
        discrete : bool
            Whether the space is inherently discrete (true) or a discretization
            of a continuous space (false).
        vol : numpy.ndarray
            An array of pixel volumes, only one component if the pixels all
            have the same volume.
Marco Selig's avatar
Marco Selig committed
217
    """
218

Ultima's avatar
Ultima committed
219
    def __init__(self):
Marco Selig's avatar
Marco Selig committed
220
        """
Ultimanet's avatar
Ultimanet committed
221
            Sets the attributes for a space class instance.
Marco Selig's avatar
Marco Selig committed
222
223
224

            Parameters
            ----------
225
            dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
226
227
                Data type of the field values for a field defined on this space
                (default: numpy.float64).
228
            datamodel :
Marco Selig's avatar
Marco Selig committed
229

Ultimanet's avatar
Ultimanet committed
230
231
232
            Returns
            -------
            None
Marco Selig's avatar
Marco Selig committed
233
        """
234
        self.paradict = space_paradict()
235

Ultimanet's avatar
Ultimanet committed
236
237
238
    @property
    def para(self):
        return self.paradict['default']
239

Ultimanet's avatar
Ultimanet committed
240
241
242
    @para.setter
    def para(self, x):
        self.paradict['default'] = x
Marco Selig's avatar
Marco Selig committed
243

244
    def _identifier(self):
Marco Selig's avatar
Marco Selig committed
245
        """
246
247
248
        _identiftier returns an object which contains all information needed
        to uniquely idetnify a space. It returns a (immutable) tuple which
        therefore can be compared.
249
        """
250
251
252
253
254
255
256
257
258
259
260
261
262
        return tuple(sorted(vars(self).items()))

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

    def __ne__(self, x):
        return not self.__eq__(x)

    def __len__(self):
        return int(self.get_dim(split=False))
Marco Selig's avatar
Marco Selig committed
263

264
    def copy(self):
265
        return space(para=self.para,
266
                     dtype=self.dtype)
Marco Selig's avatar
Marco Selig committed
267

Ultimanet's avatar
Ultimanet committed
268
    def getitem(self, data, key):
269
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
270
            "ERROR: no generic instance method 'getitem'."))
Marco Selig's avatar
Marco Selig committed
271

Ultimanet's avatar
Ultimanet committed
272
    def setitem(self, data, key):
273
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
274
            "ERROR: no generic instance method 'getitem'."))
275

Ultimanet's avatar
Ultimanet committed
276
    def apply_scalar_function(self, x, function, inplace=False):
277
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
278
            "ERROR: no generic instance method 'apply_scalar_function'."))
Marco Selig's avatar
Marco Selig committed
279

Ultimanet's avatar
Ultimanet committed
280
    def unary_operation(self, x, op=None):
281
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
282
            "ERROR: no generic instance method 'unary_operation'."))
283

Ultimanet's avatar
Ultimanet committed
284
    def binary_operation(self, x, y, op=None):
285
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
286
            "ERROR: no generic instance method 'binary_operation'."))
Marco Selig's avatar
Marco Selig committed
287

288
    def get_norm(self, x, q):
289
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
290
            "ERROR: no generic instance method 'norm'."))
Marco Selig's avatar
Marco Selig committed
291

292
    def get_shape(self):
293
        raise NotImplementedError(about._errors.cstring(
Ultimanet's avatar
Ultimanet committed
294
            "ERROR: no generic instance method 'shape'."))
Marco Selig's avatar
Marco Selig committed
295

296
    def get_dim(self, split=False):
Marco Selig's avatar
Marco Selig committed
297
        """
Ultimanet's avatar
Ultimanet committed
298
            Computes the dimension of the space, i.e.\  the number of pixels.
Marco Selig's avatar
Marco Selig committed
299
300
301

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
302
303
304
            split : bool, *optional*
                Whether to return the dimension split up, i.e. the numbers of
                pixels in each direction, or not (default: False).
Marco Selig's avatar
Marco Selig committed
305

Ultimanet's avatar
Ultimanet committed
306
307
308
309
            Returns
            -------
            dim : {int, numpy.ndarray}
                Dimension(s) of the space.
Marco Selig's avatar
Marco Selig committed
310
        """
311
        raise NotImplementedError(about._errors.cstring(
312
            "ERROR: no generic instance method 'dim'."))
Marco Selig's avatar
Marco Selig committed
313

314
    def get_dof(self):
Marco Selig's avatar
Marco Selig committed
315
        """
Ultimanet's avatar
Ultimanet committed
316
            Computes the number of degrees of freedom of the space.
Marco Selig's avatar
Marco Selig committed
317
318
319

            Returns
            -------
Ultimanet's avatar
Ultimanet committed
320
321
            dof : int
                Number of degrees of freedom of the space.
Marco Selig's avatar
Marco Selig committed
322
        """
323
        raise NotImplementedError(about._errors.cstring(
324
            "ERROR: no generic instance method 'dof'."))
Marco Selig's avatar
Marco Selig committed
325

326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
    def get_meta_volume(self, total=False):
        """
            Calculates the meta volumes.

            The meta volumes are the volumes associated with each component of
            a field, taking into account field components that are not
            explicitly included in the array of field values but are determined
            by symmetry conditions.

            Parameters
            ----------
            total : bool, *optional*
                Whether to return the total meta volume of the space or the
                individual ones of each field component (default: False).

            Returns
            -------
            mol : {numpy.ndarray, float}
                Meta volume of the field components or the complete space.
        """
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'get_meta_volume'."))

    def cast(self, x, verbose=False):
        """
            Computes valid field values from a given object, trying
            to translate the given data into a valid form. Thereby it is as
            benevolent as possible.

            Parameters
            ----------
            x : {float, numpy.ndarray, nifty.field}
                Object to be transformed into an array of valid field values.

            Returns
            -------
            x : numpy.ndarray, distributed_data_object
                Array containing the field values, which are compatible to the
                space.

            Other parameters
            ----------------
            verbose : bool, *optional*
                Whether the method should raise a warning if information is
                lost during casting (default: False).
        """
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'cast'."))
Marco Selig's avatar
Marco Selig committed
374

375
    # TODO: Move enforce power into power_indices class
376
    def enforce_power(self, spec, **kwargs):
Marco Selig's avatar
Marco Selig committed
377
        """
Ultimanet's avatar
Ultimanet committed
378
            Provides a valid power spectrum array from a given object.
Marco Selig's avatar
Marco Selig committed
379
380
381

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
382
383
384
385
            spec : {scalar, list, numpy.ndarray, nifty.field, function}
                Fiducial power spectrum from which a valid power spectrum is to
                be calculated. Scalars are interpreted as constant power
                spectra.
Marco Selig's avatar
Marco Selig committed
386
387
388

            Returns
            -------
Ultimanet's avatar
Ultimanet committed
389
390
391
392
393
394
395
396
397
398
399
400
            spec : numpy.ndarray
                Valid power spectrum.

            Other parameters
            ----------------
            size : int, *optional*
                Number of bands the power spectrum shall have (default: None).
            kindex : numpy.ndarray, *optional*
                Scale of each band.
            codomain : nifty.space, *optional*
                A compatible codomain for power indexing (default: None).
            log : bool, *optional*
401
402
                Flag specifying if the spectral binning is performed on
                logarithmic
Ultimanet's avatar
Ultimanet committed
403
404
405
406
                scale or not; if set, the number of used bins is set
                automatically (if not given otherwise); by default no binning
                is done (default: None).
            nbin : integer, *optional*
407
408
                Number of used spectral bins; if given `log` is set to
                ``False``;
Ultimanet's avatar
Ultimanet committed
409
410
411
412
413
                integers below the minimum of 3 induce an automatic setting;
                by default no binning is done (default: None).
            binbounds : {list, array}, *optional*
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
414
415
                (default: None).
            vmin : {scalar, list, ndarray, field}, *optional*
Ultimanet's avatar
Ultimanet committed
416
417
                Lower limit of the uniform distribution if ``random == "uni"``
                (default: 0).
Marco Selig's avatar
Marco Selig committed
418
419

        """
420
        raise NotImplementedError(about._errors.cstring(
421
            "ERROR: no generic instance method 'enforce_power'."))
Marco Selig's avatar
Marco Selig committed
422

423
    def check_codomain(self, codomain):
Marco Selig's avatar
Marco Selig committed
424
        """
425
            Checks whether a given codomain is compatible to the space or not.
Marco Selig's avatar
Marco Selig committed
426
427
428

            Parameters
            ----------
429
430
            codomain : nifty.space
                Space to be checked for compatibility.
Marco Selig's avatar
Marco Selig committed
431
432
433

            Returns
            -------
434
435
            check : bool
                Whether or not the given codomain is compatible to the space.
Marco Selig's avatar
Marco Selig committed
436
        """
437
        raise NotImplementedError(about._errors.cstring(
438
            "ERROR: no generic instance method 'check_codomain'."))
Marco Selig's avatar
Marco Selig committed
439

440
    def get_codomain(self, **kwargs):
Marco Selig's avatar
Marco Selig committed
441
        """
442
443
444
            Generates a compatible codomain to which transformations are
            reasonable, usually either the position basis or the basis of
            harmonic eigenmodes.
Marco Selig's avatar
Marco Selig committed
445
446
447

            Parameters
            ----------
448
449
450
451
            coname : string, *optional*
                String specifying a desired codomain (default: None).
            cozerocenter : {bool, numpy.ndarray}, *optional*
                Whether or not the grid is zerocentered for each axis or not
Ultimanet's avatar
Ultimanet committed
452
                (default: None).
453
454
455
456
            conest : list, *optional*
                List of nested spaces of the codomain (default: None).
            coorder : list, *optional*
                Permutation of the list of nested spaces (default: None).
Marco Selig's avatar
Marco Selig committed
457
458
459

            Returns
            -------
460
461
            codomain : nifty.space
                A compatible codomain.
Ultimanet's avatar
Ultimanet committed
462
        """
463
        raise NotImplementedError(about._errors.cstring(
464
            "ERROR: no generic instance method 'get_codomain'."))
Marco Selig's avatar
Marco Selig committed
465

466
    def get_random_values(self, **kwargs):
Marco Selig's avatar
Marco Selig committed
467
        """
Ultimanet's avatar
Ultimanet committed
468
469
            Generates random field values according to the specifications given
            by the parameters.
Marco Selig's avatar
Marco Selig committed
470

Ultimanet's avatar
Ultimanet committed
471
472
473
474
475
476
477
            Returns
            -------
            x : numpy.ndarray
                Valid field values.

            Other parameters
            ----------------
Marco Selig's avatar
Marco Selig committed
478
            random : string, *optional*
Ultimanet's avatar
Ultimanet committed
479
480
481
                Specifies the probability distribution from which the random
                numbers are to be drawn.
                Supported distributions are:
Marco Selig's avatar
Marco Selig committed
482
483

                - "pm1" (uniform distribution over {+1,-1} or {+1,+i,-1,-i}
484
485
                - "gau" (normal distribution with zero-mean and a given
                    standard deviation or variance)
Marco Selig's avatar
Marco Selig committed
486
487
488
489
                - "syn" (synthesizes from a given power spectrum)
                - "uni" (uniform distribution over [vmin,vmax[)

                (default: None).
Ultimanet's avatar
Ultimanet committed
490
491
492
493
494
            dev : float, *optional*
                Standard deviation (default: 1).
            var : float, *optional*
                Variance, overriding `dev` if both are specified
                (default: 1).
495
496
            spec : {scalar, list, numpy.ndarray, nifty.field, function},
                    *optional*
Ultimanet's avatar
Ultimanet committed
497
                Power spectrum (default: 1).
498
499
500
501
            pindex : numpy.ndarray, *optional*
                Indexing array giving the power spectrum index of each band
                (default: None).
            kindex : numpy.ndarray, *optional*
Ultimanet's avatar
Ultimanet committed
502
                Scale of each band (default: None).
503
            codomain : nifty.space, *optional*
Ultimanet's avatar
Ultimanet committed
504
                A compatible codomain with power indices (default: None).
505
            log : bool, *optional*
506
507
                Flag specifying if the spectral binning is performed on
                logarithmic
508
509
510
511
                scale or not; if set, the number of used bins is set
                automatically (if not given otherwise); by default no binning
                is done (default: None).
            nbin : integer, *optional*
512
513
                Number of used spectral bins; if given `log` is set to
                ``False``;
514
515
516
517
518
                integers below the minimum of 3 induce an automatic setting;
                by default no binning is done (default: None).
            binbounds : {list, array}, *optional*
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
519
520
                (default: None).
            vmin : {scalar, list, ndarray, field}, *optional*
521
522
                Lower limit of the uniform distribution if ``random == "uni"``
                (default: 0).
Ultimanet's avatar
Ultimanet committed
523
524
525
526
            vmin : float, *optional*
                Lower limit for a uniform distribution (default: 0).
            vmax : float, *optional*
                Upper limit for a uniform distribution (default: 1).
Marco Selig's avatar
Marco Selig committed
527
        """
528
529
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'get_random_values'."))
Marco Selig's avatar
Marco Selig committed
530

531
    def calc_weight(self, x, power=1):
Marco Selig's avatar
Marco Selig committed
532
        """
533
534
            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
535
536
537

            Parameters
            ----------
538
539
540
541
            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
542
543
544

            Returns
            -------
545
546
            y : numpy.ndarray
                Weighted array.
Marco Selig's avatar
Marco Selig committed
547
        """
548
        raise NotImplementedError(about._errors.cstring(
549
            "ERROR: no generic instance method 'calc_weight'."))
Marco Selig's avatar
Marco Selig committed
550

551
552
553
    def get_weight(self, power=1):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'get_weight'."))
Marco Selig's avatar
Marco Selig committed
554

555
    def calc_dot(self, x, y):
Marco Selig's avatar
Marco Selig committed
556
        """
557
558
            Computes the discrete inner product of two given arrays of field
            values.
Marco Selig's avatar
Marco Selig committed
559
560
561

            Parameters
            ----------
562
563
564
565
            x : numpy.ndarray
                First array
            y : numpy.ndarray
                Second array
Marco Selig's avatar
Marco Selig committed
566
567
568

            Returns
            -------
569
570
            dot : scalar
                Inner product of the two arrays.
Ultimanet's avatar
Ultimanet committed
571
        """
572
        raise NotImplementedError(about._errors.cstring(
573
            "ERROR: no generic instance method 'dot'."))
Marco Selig's avatar
Marco Selig committed
574

575
    def calc_transform(self, x, codomain=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
576
        """
577
            Computes the transform of a given array of field values.
Marco Selig's avatar
Marco Selig committed
578

Ultimanet's avatar
Ultimanet committed
579
580
            Parameters
            ----------
581
582
583
584
585
            x : numpy.ndarray
                Array to be transformed.
            codomain : nifty.space, *optional*
                codomain space to which the transformation shall map
                (default: self).
Marco Selig's avatar
Marco Selig committed
586
587
588

            Returns
            -------
Ultimanet's avatar
Ultimanet committed
589
590
            Tx : numpy.ndarray
                Transformed array
591

Ultimanet's avatar
Ultimanet committed
592
593
594
595
            Other parameters
            ----------------
            iter : int, *optional*
                Number of iterations performed in specific transformations.
596
        """
597
598
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'calc_transform'."))
Marco Selig's avatar
Marco Selig committed
599

600
    def calc_smooth(self, x, sigma=0, **kwargs):
Marco Selig's avatar
Marco Selig committed
601
        """
Ultimanet's avatar
Ultimanet committed
602
603
            Smoothes an array of field values by convolution with a Gaussian
            kernel.
Marco Selig's avatar
Marco Selig committed
604
605
606

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
607
608
609
610
611
            x : numpy.ndarray
                Array of field values to be smoothed.
            sigma : float, *optional*
                Standard deviation of the Gaussian kernel, specified in units
                of length in position space (default: 0).
Marco Selig's avatar
Marco Selig committed
612
613
614

            Returns
            -------
Ultimanet's avatar
Ultimanet committed
615
616
            Gx : numpy.ndarray
                Smoothed array.
Marco Selig's avatar
Marco Selig committed
617

Ultimanet's avatar
Ultimanet committed
618
619
620
621
            Other parameters
            ----------------
            iter : int, *optional*
                Number of iterations (default: 0).
Marco Selig's avatar
Marco Selig committed
622
        """
623
624
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'calc_smooth'."))
Marco Selig's avatar
Marco Selig committed
625

626
    def calc_power(self, x, **kwargs):
Marco Selig's avatar
Marco Selig committed
627
        """
Ultimanet's avatar
Ultimanet committed
628
            Computes the power of an array of field values.
Marco Selig's avatar
Marco Selig committed
629
630
631

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
632
633
634
            x : numpy.ndarray
                Array containing the field values of which the power is to be
                calculated.
Marco Selig's avatar
Marco Selig committed
635
636
637
638

            Returns
            -------
            spec : numpy.ndarray
Ultimanet's avatar
Ultimanet committed
639
                Power contained in the input array.
Marco Selig's avatar
Marco Selig committed
640
641
642

            Other parameters
            ----------------
Ultimanet's avatar
Ultimanet committed
643
644
645
            pindex : numpy.ndarray, *optional*
                Indexing array assigning the input array components to
                components of the power spectrum (default: None).
646
            kindex : numpy.ndarray, *optional*
Ultimanet's avatar
Ultimanet committed
647
648
649
650
                Scale corresponding to each band in the power spectrum
                (default: None).
            rho : numpy.ndarray, *optional*
                Number of degrees of freedom per band (default: None).
651
652
653
            codomain : nifty.space, *optional*
                A compatible codomain for power indexing (default: None).
            log : bool, *optional*
654
655
                Flag specifying if the spectral binning is performed on
                logarithmic
656
657
658
659
                scale or not; if set, the number of used bins is set
                automatically (if not given otherwise); by default no binning
                is done (default: None).
            nbin : integer, *optional*
660
661
                Number of used spectral bins; if given `log` is set to
                ``False``;
662
663
664
665
666
                integers below the minimum of 3 induce an automatic setting;
                by default no binning is done (default: None).
            binbounds : {list, array}, *optional*
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
667
668
                (default: None).
            vmin : {scalar, list, ndarray, field}, *optional*
669
670
                Lower limit of the uniform distribution if ``random == "uni"``
                (default: 0).
671

Marco Selig's avatar
Marco Selig committed
672
        """
673
674
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'calc_power'."))
Marco Selig's avatar
Marco Selig committed
675

676
677
678
679
680
681
682
    def calc_real_Q(self, x):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'calc_real_Q'."))

    def calc_bincount(self, x, weights=None, minlength=None):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'calc_bincount'."))
Marco Selig's avatar
Marco Selig committed
683

684
    def get_plot(self, x, **kwargs):
Marco Selig's avatar
Marco Selig committed
685
        """
Ultimanet's avatar
Ultimanet committed
686
687
            Creates a plot of field values according to the specifications
            given by the parameters.
688
689
690

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
            x : numpy.ndarray
                Array containing the field values.

            Returns
            -------
            None

            Other parameters
            ----------------
            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)``).
            power : bool, *optional*
                Whether to plot the power contained in the field or the field
                values themselves (default: False).
            unit : string, *optional*
                Unit of the field values (default: "").
            norm : string, *optional*
                Scaling of the field values before plotting (default: None).
            cmap : matplotlib.colors.LinearSegmentedColormap, *optional*
                Color map to be used for two-dimensional plots (default: None).
            cbar : bool, *optional*
                Whether to show the color bar or not (default: True).
            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).
            mono : bool, *optional*
                Whether to plot the monopole or not (default: True).
            save : string, *optional*
                Valid file name where the figure is to be stored, by default
                the figure is not saved (default: False).
            error : {float, numpy.ndarray, nifty.field}, *optional*
                Object indicating some confidence interval to be plotted
                (default: None).
            kindex : numpy.ndarray, *optional*
                Scale corresponding to each band in the power spectrum
                (default: None).
            codomain : nifty.space, *optional*
                A compatible codomain for power indexing (default: None).
            log : bool, *optional*
736
737
                Flag specifying if the spectral binning is performed on
                logarithmic
738
739
740
                scale or not; if set, the number of used bins is set
                automatically (if not given otherwise); by default no binning
                is done (default: None).
Ultimanet's avatar
Ultimanet committed
741
            nbin : integer, *optional*
742
743
                Number of used spectral bins; if given `log` is set to
                ``False``;
744
                integers below the minimum of 3 induce an automatic setting;
745
                by default no binning is done (default: None).
Ultimanet's avatar
Ultimanet committed
746
            binbounds : {list, array}, *optional*
747
748
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
749
750
                (default: None).
            vmin : {scalar, list, ndarray, field}, *optional*
Ultimanet's avatar
Ultimanet committed
751
752
753
754
                Lower limit of the uniform distribution if ``random == "uni"``
                (default: 0).
            iter : int, *optional*
                Number of iterations (default: 0).
Marco Selig's avatar
Marco Selig committed
755
756

        """
757
758
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'get_plot'."))
Marco Selig's avatar
Marco Selig committed
759

Ultimanet's avatar
Ultimanet committed
760
761
    def __repr__(self):
        return "<nifty_core.space>"
Marco Selig's avatar
Marco Selig committed
762

Ultimanet's avatar
Ultimanet committed
763
    def __str__(self):
764
765
        return "nifty_core.space instance\n- para     = " + str(self.para) + \
            "\n- dtype = " + str(self.dtype.type)
Marco Selig's avatar
Marco Selig committed
766
767


Ultimanet's avatar
Ultimanet committed
768
class point_space(space):
Marco Selig's avatar
Marco Selig committed
769
    """
Ultimanet's avatar
Ultimanet committed
770
771
772
773
774
775
776
        ..                            __             __
        ..                          /__/           /  /_
        ..      ______    ______    __   __ ___   /   _/
        ..    /   _   | /   _   | /  / /   _   | /  /
        ..   /  /_/  / /  /_/  / /  / /  / /  / /  /_
        ..  /   ____/  \______/ /__/ /__/ /__/  \___/  space class
        .. /__/
Marco Selig's avatar
Marco Selig committed
777

Ultimanet's avatar
Ultimanet committed
778
        NIFTY subclass for unstructured spaces.
Marco Selig's avatar
Marco Selig committed
779

Ultimanet's avatar
Ultimanet committed
780
781
        Unstructured spaces are lists of values without any geometrical
        information.
Marco Selig's avatar
Marco Selig committed
782
783
784

        Parameters
        ----------
Ultimanet's avatar
Ultimanet committed
785
786
        num : int
            Number of points.
787
        dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
788
            Data type of the field values (default: None).
Marco Selig's avatar
Marco Selig committed
789

Ultimanet's avatar
Ultimanet committed
790
        Attributes
Marco Selig's avatar
Marco Selig committed
791
        ----------
Ultimanet's avatar
Ultimanet committed
792
793
        para : numpy.ndarray
            Array containing the number of points.
794
        dtype : numpy.dtype
Ultimanet's avatar
Ultimanet committed
795
796
797
798
799
800
            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
801
    """
802

803
804
    def __init__(self, num, dtype=np.dtype('float'), datamodel='fftw',
                 comm=gc['default_comm']):
Ultimanet's avatar
Ultimanet committed
805
806
        """
            Sets the attributes for a point_space class instance.
Marco Selig's avatar
Marco Selig committed
807

Ultimanet's avatar
Ultimanet committed
808
809
810
811
            Parameters
            ----------
            num : int
                Number of points.
812
            dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
813
                Data type of the field values (default: numpy.float64).
Marco Selig's avatar
Marco Selig committed
814

Ultimanet's avatar
Ultimanet committed
815
816
817
818
            Returns
            -------
            None.
        """
819
820
        self.paradict = point_space_paradict(num=num)

821
822
        # parse dtype
        dtype = np.dtype(dtype)
Ultima's avatar
Ultima committed
823
824
825
826
827
828
829
830
831
        if dtype not in [np.dtype('bool'),
                         np.dtype('int16'),
                         np.dtype('int32'),
                         np.dtype('int64'),
                         np.dtype('float32'),
                         np.dtype('float64'),
                         np.dtype('complex64'),
                         np.dtype('complex128')]:
            raise ValueError(about._errors.cstring(
832
                             "WARNING: incompatible dtype: " + str(dtype)))
Ultima's avatar
Ultima committed
833
        self.dtype = dtype
834
835

        if datamodel not in ['np'] + POINT_DISTRIBUTION_STRATEGIES:
Ultima's avatar
Ultima committed
836
            about._errors.cstring("WARNING: datamodel set to default.")
837
            self.datamodel = \
838
                gc['default_distribution_strategy']
839
840
        else:
            self.datamodel = datamodel
841

842
        self.comm = self._parse_comm(comm)
Ultimanet's avatar
Ultimanet committed
843
        self.discrete = True
844
        self.harmonic = False
845
        self.distances = (np.float(1),)
Marco Selig's avatar
Marco Selig committed
846

Ultimanet's avatar
Ultimanet committed
847
848
849
850
    @property
    def para(self):
        temp = np.array([self.paradict['num']], dtype=int)
        return temp
851

Ultimanet's avatar
Ultimanet committed
852
853
    @para.setter
    def para(self, x):
Ultima's avatar
Ultima committed
854
        self.paradict['num'] = x[0]
855

856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
    def _identifier(self):
        # Extract the identifying parts from the vars(self) dict.
        temp = [(ii[0],
                 ((lambda x: x[1].__hash__() if x[0] == 'comm' else x)(ii)))
                for ii in vars(self).iteritems()
                ]
        # Return the sorted identifiers as a tuple.
        return tuple(sorted(temp))

    def _parse_comm(self, comm):
        # check if comm is a string -> the name of comm is given
        # -> Extract it from the mpi_module
        if isinstance(comm, str):
            if gc.validQ('default_comm', comm):
                result_comm = getattr(gdi[gc['mpi_module']], comm)
            else:
                raise ValueError(about._errors.cstring(
                    "ERROR: The given communicator-name is not supported."))
        # check if the given comm object is an instance of default Intracomm
        else:
            if isinstance(comm, gdi[gc['mpi_module']].Intracomm):
                result_comm = comm
            else:
                raise ValueError(about._errors.cstring(
                    "ERROR: The given comm object is not an instance of the " +
                    "default-MPI-module's Intracomm Class."))
        return result_comm

884
    def copy(self):
885
        return point_space(num=self.paradict['num'],
886
                           dtype=self.dtype,
887
888
                           datamodel=self.datamodel,
                           comm=self.comm)
889

Ultimanet's avatar
Ultimanet committed
890
891
    def getitem(self, data, key):
        return data[key]
Marco Selig's avatar
Marco Selig committed
892

Ultimanet's avatar
Ultimanet committed
893
    def setitem(self, data, update, key):
894
        data[key] = update
Marco Selig's avatar
Marco Selig committed
895

Ultimanet's avatar
Ultimanet committed
896
    def apply_scalar_function(self, x, function, inplace=False):
897
        if self.datamodel == 'np':
898
            if not inplace:
899
                try:
900
901
902
903
904
905
906
907
908
                    return function(x)
                except:
                    return np.vectorize(function)(x)
            else:
                try:
                    x[:] = function(x)
                except:
                    x[:] = np.vectorize(function)(x)
                return x
909
910

        elif self.datamodel in POINT_DISTRIBUTION_STRATEGIES:
911
            return x.apply_scalar_function(function, inplace=inplace)
Ultimanet's avatar
Ultimanet committed
912
        else:
913
914
915
            raise NotImplementedError(about._errors.cstring(
                "ERROR: function is not implemented for given datamodel."))

Ultimanet's avatar
Ultimanet committed
916
917
918
919
    def unary_operation(self, x, op='None', **kwargs):
        """
        x must be a numpy array which is compatible with the space!
        Valid operations are
920

Ultimanet's avatar
Ultimanet committed
921
        """
922
        if self.datamodel == 'np':
923
924
925
926
            def _argmin(z, **kwargs):
                ind = np.argmin(z, **kwargs)
                if np.isscalar(ind):
                    ind = np.unravel_index(ind, z.shape, order='C')
927
                    if(len(ind) == 1):
928
                        return ind[0]
929
930
                return ind

931
932
933
934
            def _argmax(z, **kwargs):
                ind = np.argmax(z, **kwargs)
                if np.isscalar(ind):
                    ind = np.unravel_index(ind, z.shape, order='C')
935
                    if(len(ind) == 1):
936
                        return ind[0]
937
938
                return ind

Ultima's avatar
Ultima committed
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
            translation = {'pos': lambda y: getattr(y, '__pos__')(),
                           'neg': lambda y: getattr(y, '__neg__')(),
                           'abs': lambda y: getattr(y, '__abs__')(),
                           'real': lambda y: getattr(y, 'real'),
                           'imag': lambda y: getattr(y, 'imag'),
                           'nanmin': np.nanmin,
                           'amin': np.amin,
                           'nanmax': np.nanmax,
                           'amax': np.amax,
                           'median': np.median,
                           'mean': np.mean,
                           'std': np.std,
                           'var': np.var,
                           'argmin': _argmin,
                           'argmin_flat': np.argmin,
                           'argmax': _argmax,
                           'argmax_flat': np.argmax,
                           'conjugate': np.conjugate,
                           'sum': np.sum,
                           'prod': np.prod,
                           'unique': np.unique,
                           'copy': np.copy,
                           'copy_empty': np.empty_like,
                           'isnan': np.isnan,
                           'isinf': np.isinf,
                           'isfinite': np.isfinite,
                           'nan_to_num': np.nan_to_num,
                           'all': np.all,
                           'any': np.any,
                           'None': lambda y: y}
969
970

        elif self.datamodel in POINT_DISTRIBUTION_STRATEGIES:
Ultima's avatar
Ultima committed
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
            translation = {'pos': lambda y: getattr(y, '__pos__')(),
                           'neg': lambda y: getattr(y, '__neg__')(),
                           'abs': lambda y: getattr(y, '__abs__')(),
                           'real': lambda y: getattr(y, 'real'),
                           'imag': lambda y: getattr(y, 'imag'),
                           'nanmin': lambda y: getattr(y, 'nanmin')(),
                           'amin': lambda y: getattr(y, 'amin')(),
                           'nanmax': lambda y: getattr(y, 'nanmax')(),
                           'amax': lambda y: getattr(y, 'amax')(),
                           'median': lambda y: getattr(y, 'median')(),
                           'mean': lambda y: getattr(y, 'mean')(),
                           'std': lambda y: getattr(y, 'std')(),
                           'var': lambda y: getattr(y, 'var')(),
                           'argmin': lambda y: getattr(y, 'argmin_nonflat')(),
                           'argmin_flat': lambda y: getattr(y, 'argmin')(),
                           'argmax': lambda y: getattr(y, 'argmax_nonflat')(),
                           'argmax_flat': lambda y: getattr(y, 'argmax')(),
                           'conjugate': lambda y: getattr(y, 'conjugate')(),
                           'sum': lambda y: getattr(y, 'sum')(),
                           'prod': lambda y: getattr(y, 'prod')(),
                           'unique': lambda y: getattr(y, 'unique')(),
                           'copy': lambda y: getattr(y, 'copy')(),
                           'copy_empty': lambda y: getattr(y, 'copy_empty')(),
                           'isnan': lambda y: getattr(y, 'isnan')(),
                           'isinf': lambda y: getattr(y, 'isinf')(),
                           'isfinite': lambda y: getattr(y, 'isfinite')(),
                           'nan_to_num': lambda y: getattr(y, 'nan_to_num')(),
                           'all': lambda y: getattr(y, 'all')(),
                           'any': lambda y: getattr(y, 'any')(),
                           'None': lambda y: y}
1001
1002
1003
        else:
            raise NotImplementedError(about._errors.cstring(
                "ERROR: function is not implemented for given datamodel."))
Marco Selig's avatar
Marco Selig committed
1004

1005
1006
        return translation[op](x, **kwargs)

Ultimanet's avatar
Ultimanet committed
1007
    def binary_operation(self, x, y, op='None', cast=0):
1008

Ultima's avatar
Ultima committed
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
        translation = {'add': lambda z: getattr(z, '__add__'),
                       'radd': lambda z: getattr(z, '__radd__'),
                       'iadd': lambda z: getattr(z, '__iadd__'),
                       'sub': lambda z: getattr(z, '__sub__'),
                       'rsub': lambda z: getattr(z, '__rsub__'),
                       'isub': lambda z: getattr(z, '__isub__'),
                       'mul': lambda z: getattr(z, '__mul__'),
                       'rmul': lambda z: getattr(z, '__rmul__'),
                       'imul': lambda z: getattr(z, '__imul__'),
                       'div': lambda z: getattr(z, '__div__'),
                       'rdiv': lambda z: getattr(z, '__rdiv__'),
                       'idiv': lambda z: getattr(z, '__idiv__'),
                       'pow': lambda z: getattr(z, '__pow__'),
                       'rpow': lambda z: getattr(z, '__rpow__'),
                       'ipow': lambda z: getattr(z, '__ipow__'),
                       'ne': lambda z: getattr(z, '__ne__'),
                       'lt': lambda z: getattr(z, '__lt__'),
                       'le': lambda z: getattr(z, '__le__'),
                       'eq': lambda z: getattr(z, '__eq__'),
                       'ge': lambda z: getattr(z, '__ge__'),
                       'gt': lambda z: getattr(z, '__gt__'),
                       'None': lambda z: lambda u: u}
1031

Ultimanet's avatar
Ultimanet committed
1032
1033
1034
        if (cast & 1) != 0:
            x = self.cast(x)
        if (cast & 2) != 0:
1035
1036
            y = self.cast(y)

Ultimanet's avatar
Ultimanet committed
1037
        return translation[op](x)(y)
Marco Selig's avatar
Marco Selig committed
1038

1039
    def get_norm(self, x, q=2):
Ultimanet's avatar
Ultimanet committed
1040
1041
        """
            Computes the Lq-norm of field values.
Marco Selig's avatar
Marco Selig committed
1042

Ultimanet's avatar
Ultimanet committed
1043
1044
            Parameters
            ----------
1045
1046
            x : np.ndarray
                The data array
Ultimanet's avatar
Ultimanet committed
1047
1048
            q : scalar
                Parameter q of the Lq-norm (default: 2).
Marco Selig's avatar
Marco Selig committed
1049

Ultimanet's avatar
Ultimanet committed
1050
1051
1052
1053
            Returns
            -------
            norm : scalar
                The Lq-norm of the field values.
Marco Selig's avatar
Marco Selig committed
1054

Ultimanet's avatar
Ultimanet committed
1055
        """
1056
        if q == 2:
1057
            result = self.calc_dot(x, x)
Ultimanet's avatar
Ultimanet committed
1058
        else:
1059
1060
            y = x**(q - 1)
            result = self.calc_dot(x, y)
Marco Selig's avatar
Marco Selig committed
1061

1062
1063
        result = result**(1. / q)
        return result
Marco Selig's avatar
Marco Selig committed
1064

1065
    def get_shape(self):
1066
        return (self.paradict['num'],)
Marco Selig's avatar
Marco Selig committed
1067

Ultima's avatar
Ultima committed
1068
    def get_dim(self):
Ultimanet's avatar
Ultimanet committed
1069
1070
        """
            Computes the dimension of the space, i.e.\  the number of points.
Marco Selig's avatar
Marco Selig committed
1071

Ultimanet's avatar
Ultimanet committed
1072
1073
1074
1075
1076
            Parameters
            ----------
            split : bool, *optional*
                Whether to return the dimension as an array with one component
                or as a scalar (default: False).
Marco Selig's avatar
Marco Selig committed
1077

Ultimanet's avatar
Ultimanet committed
1078
1079
1080
1081
1082
            Returns
            -------
            dim : {int, numpy.ndarray}
                Dimension(s) of the space.
        """
Ultima's avatar
Ultima committed
1083
        return np.prod(self.get_shape())
Marco Selig's avatar
Marco Selig committed
1084

1085
    def get_dof(self, split=False):
Ultimanet's avatar
Ultimanet committed
1086
1087
1088
1089
        """
            Computes the number of degrees of freedom of the space, i.e./  the
            number of points for real-valued fields and twice that number for
            complex-valued fields.
Marco Selig's avatar
Marco Selig committed
1090

Ultimanet's avatar
Ultimanet committed
1091
1092
1093
1094
1095
            Returns
            -------
            dof : int
                Number of degrees of freedom of the space.
        """
Ultima's avatar
Ultima committed
1096
1097
1098
1099
        if split:
            dof = self.get_shape()
            if issubclass(self.dtype.type, np.complexfloating):
                dof = tuple(np.array(dof)*2)
1100
        else:
Ultima's avatar
Ultima committed
1101
1102
1103
1104
            dof = self.get_dim()
            if issubclass(self.dtype.type, np.complexfloating):
                dof = dof * 2
        return dof
1105
1106
1107
1108

    def get_vol(self, split=False):
        if split:
            return self.distances
Ultimanet's avatar
Ultimanet committed
1109
        else:
1110
            return np.prod(self.distances)
Marco Selig's avatar
Marco Selig committed
1111

1112
    def get_meta_volume(self, split=False):
Marco Selig's avatar
Marco Selig committed
1113
        """
1114
            Calculates the meta volumes.
Ultimanet's avatar
Ultimanet committed
1115

1116
1117
1118
1119
1120
            The meta volumes are the volumes associated with each component of
            a field, taking into account field components that are not
            explicitly included in the array of field values but are determined
            by symmetry conditions. In the case of an :py:class:`rg_space`, the
            meta volumes are simply the pixel volumes.
Marco Selig's avatar
Marco Selig committed
1121
1122
1123

            Parameters
            ----------
1124
1125
1126
            total : bool, *optional*
                Whether to return the total meta volume of the space or the
                individual ones of each pixel (default: False).
Marco Selig's avatar
Marco Selig committed
1127
1128
1129

            Returns
            -------
1130
1131
            mol : {numpy.ndarray, float}
                Meta volume of the pixels or the complete space.
Ultimanet's avatar
Ultimanet committed
1132
        """