nifty_rg.py 74.7 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) 2015 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

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

Marco Selig's avatar
Marco Selig committed
31
    NIFTY submodule for regular Cartesian grids.
Marco Selig's avatar
Marco Selig committed
32
33
34

"""
from __future__ import division
Ultimanet's avatar
Ultimanet committed
35

36
import itertools
Marco Selig's avatar
Marco Selig committed
37
import numpy as np
38
import os
39
from scipy.special import erf
Marco Selig's avatar
Marco Selig committed
40
41
42
import pylab as pl
from matplotlib.colors import LogNorm as ln
from matplotlib.ticker import LogFormatter as lf
Ultimanet's avatar
Ultimanet committed
43

44
45
46
from nifty.nifty_core import point_space,\
                             field
import nifty_fft
47
from nifty.keepers import about,\
Ultima's avatar
Ultima committed
48
49
                          global_dependency_injector as gdi,\
                          global_configuration as gc
theos's avatar
theos committed
50
51
from nifty.d2o import distributed_data_object,\
                      STRATEGIES as DISTRIBUTION_STRATEGIES
Ultimanet's avatar
Ultimanet committed
52
from nifty.nifty_paradict import rg_space_paradict
53
54
from nifty.nifty_power_indices import rg_power_indices
from nifty.nifty_random import random
Ultima's avatar
Ultima committed
55
import nifty.nifty_utilities as utilities
56

Ultima's avatar
Ultima committed
57
MPI = gdi[gc['mpi_module']]
58
RG_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']
Ultimanet's avatar
Ultimanet committed
59

Marco Selig's avatar
Marco Selig committed
60

61
class rg_space(point_space):
Marco Selig's avatar
Marco Selig committed
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
    """
        ..      _____   _______
        ..    /   __/ /   _   /
        ..   /  /    /  /_/  /
        ..  /__/     \____  /  space class
        ..          /______/

        NIFTY subclass for spaces of regular Cartesian grids.

        Parameters
        ----------
        num : {int, numpy.ndarray}
            Number of gridpoints or numbers of gridpoints along each axis.
        naxes : int, *optional*
            Number of axes (default: None).
        zerocenter : {bool, numpy.ndarray}, *optional*
            Whether the Fourier zero-mode is located in the center of the grid
            (or the center of each axis speparately) or not (default: True).
        hermitian : bool, *optional*
            Whether the fields living in the space follow hermitian symmetry or
            not (default: True).
        purelyreal : bool, *optional*
            Whether the field values are purely real (default: True).
        dist : {float, numpy.ndarray}, *optional*
            Distance between two grid points along each axis (default: None).
        fourier : bool, *optional*
            Whether the space represents a Fourier or a position grid
            (default: False).

        Notes
        -----
        Only even numbers of grid points per axis are supported.
        The basis transformations between position `x` and Fourier mode `k`
        rely on (inverse) fast Fourier transformations using the
        :math:`exp(2 \pi i k^\dagger x)`-formulation.

        Attributes
        ----------
        para : numpy.ndarray
            One-dimensional array containing information on the axes of the
            space in the following form: The first entries give the grid-points
            along each axis in reverse order; the next entry is 0 if the
            fields defined on the space are purely real-valued, 1 if they are
            hermitian and complex, and 2 if they are not hermitian, but
            complex-valued; the last entries hold the information on whether
            the axes are centered on zero or not, containing a one for each
            zero-centered axis and a zero for each other one, in reverse order.
109
        dtype : numpy.dtype
Marco Selig's avatar
Marco Selig committed
110
111
112
113
114
115
116
117
118
119
120
121
            Data type of the field values for a field defined on this space,
            either ``numpy.float64`` or ``numpy.complex128``.
        discrete : bool
            Whether or not the underlying space is discrete, always ``False``
            for regular grids.
        vol : numpy.ndarray
            One-dimensional array containing the distances between two grid
            points along each axis, in reverse order. By default, the total
            length of each axis is assumed to be one.
        fourier : bool
            Whether or not the grid represents a Fourier basis.
    """
122
    epsilon = 0.0001  # relative precision for comparisons
Marco Selig's avatar
Marco Selig committed
123

124
    def __init__(self, shape, zerocenter=False, complexity=0, distances=None,
Ultima's avatar
Ultima committed
125
                 harmonic=False, datamodel='fftw', fft_module=gc['fft_module'],
126
                 comm=gc['default_comm']):
Marco Selig's avatar
Marco Selig committed
127
128
129
130
131
132
133
134
135
136
137
138
        """
            Sets the attributes for an rg_space class instance.

            Parameters
            ----------
            num : {int, numpy.ndarray}
                Number of gridpoints or numbers of gridpoints along each axis.
            naxes : int, *optional*
                Number of axes (default: None).
            zerocenter : {bool, numpy.ndarray}, *optional*
                Whether the Fourier zero-mode is located in the center of the
                grid (or the center of each axis speparately) or not
Ultimanet's avatar
Ultimanet committed
139
                (default: False).
Marco Selig's avatar
Marco Selig committed
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
            hermitian : bool, *optional*
                Whether the fields living in the space follow hermitian
                symmetry or not (default: True).
            purelyreal : bool, *optional*
                Whether the field values are purely real (default: True).
            dist : {float, numpy.ndarray}, *optional*
                Distance between two grid points along each axis
                (default: None).
            fourier : bool, *optional*
                Whether the space represents a Fourier or a position grid
                (default: False).

            Returns
            -------
            None
        """
Ultima's avatar
Ultima committed
156
        self._cache_dict = {'check_codomain':{}}
157
        self.paradict = rg_space_paradict(shape=shape,
158
159
                                          complexity=complexity,
                                          zerocenter=zerocenter)
160
        # set dtype
161
        if self.paradict['complexity'] == 0:
162
            self.dtype = np.dtype('float64')
Marco Selig's avatar
Marco Selig committed
163
        else:
164
            self.dtype = np.dtype('complex128')
165
166
167

        # set datamodel
        if datamodel not in ['np'] + RG_DISTRIBUTION_STRATEGIES:
168
            about.warnings.cprint("WARNING: datamodel set to default.")
169
            self.datamodel = \
Ultima's avatar
Ultima committed
170
                gc['default_distribution_strategy']
171
172
173
        else:
            self.datamodel = datamodel

174
        # set volume/distances
175
176
177
178
179
        naxes = len(self.paradict['shape'])
        if distances is None:
            distances = 1 / np.array(self.paradict['shape'], dtype=np.float)
        elif np.isscalar(distances):
            distances = np.ones(naxes, dtype=np.float) * distances
Marco Selig's avatar
Marco Selig committed
180
        else:
181
182
183
184
            distances = np.array(distances, dtype=np.float)
            if np.size(distances) == 1:
                distances = distances * np.ones(naxes, dtype=np.float)
            if np.size(distances) != naxes:
185
                raise ValueError(about._errors.cstring(
186
187
188
                    "ERROR: size mismatch ( " + str(np.size(distances)) +
                    " <> " + str(naxes) + " )."))
        if np.any(distances <= 0):
189
            raise ValueError(about._errors.cstring(
190
                "ERROR: nonpositive distance(s)."))
Marco Selig's avatar
Marco Selig committed
191

192
        self.distances = tuple(distances)
193
194
195
196
        self.harmonic = bool(harmonic)
        self.discrete = False

        self.comm = self._parse_comm(comm)
Ultima's avatar
Ultima committed
197

198
199
        # Initializes the fast-fourier-transform machine, which will be used
        # to transform the space
Ultima's avatar
Ultima committed
200
        if not gc.validQ('fft_module', fft_module):
201
            about.warnings.cprint("WARNING: fft_module set to default.")
Ultima's avatar
Ultima committed
202
203
            fft_module = gc['fft_module']
        self.fft_machine = nifty_fft.fft_factory(fft_module)
204
205
206
207

        # Initialize the power_indices object which takes care of kindex,
        # pindex, rho and the pundex for a given set of parameters
        if self.harmonic:
208
209
            self.power_indices = rg_power_indices(
                    shape=self.get_shape(),
210
                    dgrid=distances,
211
212
213
214
                    zerocentered=self.paradict['zerocenter'],
                    comm=self.comm,
                    datamodel=self.datamodel,
                    allowed_distribution_strategies=RG_DISTRIBUTION_STRATEGIES)
215

216
217
    @property
    def para(self):
218
        temp = np.array(self.paradict['shape'] +
219
220
                        [self.paradict['complexity']] +
                        self.paradict['zerocenter'], dtype=int)
221
        return temp
222

223
224
    @para.setter
    def para(self, x):
225
        self.paradict['shape'] = x[:(np.size(x) - 1) // 2]
226
227
        self.paradict['zerocenter'] = x[(np.size(x) + 1) // 2:]
        self.paradict['complexity'] = x[(np.size(x) - 1) // 2]
Ultimanet's avatar
Ultimanet committed
228

Ultima's avatar
Ultima committed
229
230
231
    def __hash__(self):
        result_hash = 0
        for (key, item) in vars(self).items():
Ultima's avatar
Ultima committed
232
            if key in ['_cache_dict', 'fft_machine', 'power_indices']:
Ultima's avatar
Ultima committed
233
234
235
236
                continue
            result_hash ^= item.__hash__() * hash(key)
        return result_hash

237
238
239
240
241
242
243
244
245
246
247
    # __identiftier__ returns an object which contains all information needed
    # to uniquely identify a space. It returns a (immutable) tuple which
    # therefore can be compared.
    # The rg_space version of __identifier__ filters out the vars-information
    # which is describing the rg_space's structure
    def _identifier(self):
        # Extract the identifying parts from the vars(self) dict.
        temp = [(ii[0],
                 ((lambda x: tuple(x) if
                  isinstance(x, np.ndarray) else x)(ii[1])))
                for ii in vars(self).iteritems()
Ultima's avatar
Ultima committed
248
249
                if ii[0] not in ['_cache_dict', 'fft_machine',
                                 'power_indices', 'comm']]
250
251
252
        temp.append(('comm', self.comm.__hash__()))
        # Return the sorted identifiers as a tuple.
        return tuple(sorted(temp))
Ultimanet's avatar
Ultimanet committed
253

254
    def copy(self):
255
        return rg_space(shape=self.paradict['shape'],
256
257
                        complexity=self.paradict['complexity'],
                        zerocenter=self.paradict['zerocenter'],
258
                        distances=self.distances,
259
                        harmonic=self.harmonic,
260
                        datamodel=self.datamodel,
261
                        fft_module=self.fft_machine.name,
262
                        comm=self.comm)
263
264

    def get_shape(self):
265
        return tuple(self.paradict['shape'])
Marco Selig's avatar
Marco Selig committed
266

267
268
269
270
    def _cast_to_d2o(self, x, dtype=None, hermitianize=True, **kwargs):
        casted_x = super(rg_space, self)._cast_to_d2o(x=x,
                                                      dtype=dtype,
                                                      **kwargs)
Ultima's avatar
Ultima committed
271
        if x is not None and hermitianize and \
Ultima's avatar
Ultima committed
272
                self.paradict['complexity'] == 1 and not casted_x.hermitian:
273
274
275
276
            about.warnings.cflush(
                 "WARNING: Data gets hermitianized. This operation is " +
                 "extremely expensive\n")
            casted_x = utilities.hermitianize(casted_x)
Marco Selig's avatar
Marco Selig committed
277

278
        return casted_x
279

280
281
282
283
    def _cast_to_np(self, x, dtype=None, hermitianize=True, **kwargs):
        casted_x = super(rg_space, self)._cast_to_np(x=x,
                                                     dtype=dtype,
                                                     **kwargs)
Ultima's avatar
Ultima committed
284
        if x is not None and hermitianize and self.paradict['complexity'] == 1:
285
286
287
288
            about.warnings.cflush(
                 "WARNING: Data gets hermitianized. This operation is " +
                 "extremely expensive\n")
            casted_x = utilities.hermitianize(casted_x)
Marco Selig's avatar
Marco Selig committed
289

290
        return casted_x
ultimanet's avatar
ultimanet committed
291

292
    def enforce_power(self, spec, size=None, kindex=None, codomain=None,
Ultima's avatar
Ultima committed
293
                      **kwargs):
Marco Selig's avatar
Marco Selig committed
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
        """
            Provides a valid power spectrum array from a given object.

            Parameters
            ----------
            spec : {float, 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.

            Returns
            -------
            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*
318
319
320
                Flag specifying if the spectral binning is performed on
                logarithmic scale or not; if set, the number of used bins is
                set automatically (if not given otherwise); by default no
321
                binning is done (default: None).
Marco Selig's avatar
Marco Selig committed
322
            nbin : integer, *optional*
323
                Number of used spectral bins; if given `log` is set to
324
325
                ``False``; iintegers below the minimum of 3 induce an automatic
                setting; by default no binning is done (default: None).
Marco Selig's avatar
Marco Selig committed
326
327
328
            binbounds : {list, array}, *optional*
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
329
                (default: None).
Marco Selig's avatar
Marco Selig committed
330
        """
331
332
333
334
335
336
337

        # Setting up the local variables: kindex
        # The kindex is only necessary if spec is a function or if
        # the size is not set explicitly
        if kindex is None and (size is None or callable(spec)):
            # Determine which space should be used to get the kindex
            if self.harmonic:
338
339
                kindex_supply_space = self
            else:
340
341
                # Check if the given codomain is compatible with the space
                try:
342
343
344
                    assert(self.check_codomain(codomain))
                    kindex_supply_space = codomain
                except(AssertionError):
345
346
347
348
                    about.warnings.cprint("WARNING: Supplied codomain is " +
                                          "incompatible. Generating a " +
                                          "generic codomain. This can " +
                                          "be expensive!")
349
                    kindex_supply_space = self.get_codomain()
Ultima's avatar
Ultima committed
350

351
            kindex = kindex_supply_space.\
Ultima's avatar
Ultima committed
352
                power_indices.get_index_dict(**kwargs)['kindex']
353

354
355
356
        return self._enforce_power_helper(spec=spec,
                                          size=size,
                                          kindex=kindex)
357

Ultima's avatar
Ultima committed
358
    def _check_codomain(self, codomain):
Marco Selig's avatar
Marco Selig committed
359
        """
360
            Checks whether a given codomain is compatible to the space or not.
Marco Selig's avatar
Marco Selig committed
361
362
363

            Parameters
            ----------
364
365
            codomain : nifty.space
                Space to be checked for compatibility.
Marco Selig's avatar
Marco Selig committed
366
367
368

            Returns
            -------
369
370
            check : bool
                Whether or not the given codomain is compatible to the space.
Marco Selig's avatar
Marco Selig committed
371
        """
372
373
        if codomain is None:
            return False
374

375
        if not isinstance(codomain, rg_space):
376
377
            raise TypeError(about._errors.cstring(
                "ERROR: The given codomain must be a nifty rg_space."))
378

379
380
        if self.datamodel is not codomain.datamodel:
            return False
381

382
383
384
        if self.comm is not codomain.comm:
            return False

385
        # check number of number and size of axes
386
387
        if not np.all(np.array(self.paradict['shape']) ==
                      np.array(codomain.paradict['shape'])):
388
            return False
Ultima's avatar
Ultima committed
389

390
391
392
        # check harmonic flag
        if self.harmonic == codomain.harmonic:
            return False
Ultima's avatar
Ultima committed
393

394
395
396
397
        # check complexity-type
        # prepare the shorthands
        dcomp = self.paradict['complexity']
        cocomp = codomain.paradict['complexity']
Ultima's avatar
Ultima committed
398

399
400
401
402
403
404
405
406
407
408
409
410
411
412
        # Case 1: if the domain is copmleteley complex
        # -> the codomain must be complex, too
        if dcomp == 2:
            if cocomp != 2:
                return False
        # Case 2: domain is hermitian
        # -> codmomain can be real. If it is marked as hermitian or even
        # fully complex, a warning is raised
        elif dcomp == 1:
            if cocomp > 0:
                about.warnings.cprint("WARNING: Unrecommended codomain! " +
                                      "The domain is hermitian, hence the " +
                                      "codomain should be restricted to " +
                                      "real values!")
Ultima's avatar
Ultima committed
413

414
415
416
417
418
419
420
421
422
423
        # Case 3: domain is real
        # -> codmain should be hermitian
        elif dcomp == 0:
            if cocomp == 2:
                about.warnings.cprint("WARNING: Unrecommended codomain! " +
                                      "The domain is real, hence the " +
                                      "codomain should be restricted to " +
                                      "hermitian configurations!")
            elif cocomp == 0:
                return False
Ultima's avatar
Ultima committed
424

425
426
        # Check if the distances match, i.e. dist'=1/(num*dist)
        if not np.all(
427
                np.absolute(np.array(self.paradict['shape']) *
428
429
430
                            np.array(self.distances) *
                            np.array(codomain.distances) - 1) < self.epsilon):
            return False
Ultima's avatar
Ultima committed
431

432
        return True
433

434
    def get_codomain(self, cozerocenter=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
435
        """
436
437
438
            Generates a compatible codomain to which transformations are
            reasonable, i.e.\  either a shifted grid or a Fourier conjugate
            grid.
Marco Selig's avatar
Marco Selig committed
439
440
441

            Parameters
            ----------
442
443
444
445
446
            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
                (default: None).
Marco Selig's avatar
Marco Selig committed
447
448
449

            Returns
            -------
450
451
            codomain : nifty.rg_space
                A compatible codomain.
Marco Selig's avatar
Marco Selig committed
452

453
454
455
456
457
458
            Notes
            -----
            Possible arguments for `coname` are ``'f'`` in which case the
            codomain arises from a Fourier transformation, ``'i'`` in which
            case it arises from an inverse Fourier transformation.If no
            `coname` is given, the Fourier conjugate grid is produced.
Marco Selig's avatar
Marco Selig committed
459
        """
460
461
462
463
464
465
466
467
        naxes = len(self.get_shape())
        # Parse the cozerocenter input
        if(cozerocenter is None):
            cozerocenter = self.paradict['zerocenter']
        # if the input is something scalar, cast it to a boolean
        elif(np.isscalar(cozerocenter)):
            cozerocenter = bool(cozerocenter)
        # if it is not a scalar...
Marco Selig's avatar
Marco Selig committed
468
        else:
469
470
471
472
473
474
475
476
477
478
479
            # ...cast it to a numpy array of booleans
            cozerocenter = np.array(cozerocenter, dtype=np.bool)
            # if it was a list of length 1, extract the boolean
            if(np.size(cozerocenter) == 1):
                cozerocenter = np.asscalar(cozerocenter)
            # if the length of the input does not match the number of
            # dimensions, raise an exception
            elif(np.size(cozerocenter) != naxes):
                raise ValueError(about._errors.cstring(
                    "ERROR: size mismatch ( " +
                    str(np.size(cozerocenter)) + " <> " + str(naxes) + " )."))
Marco Selig's avatar
Marco Selig committed
480

481
        # Set up the initialization variables
482
483
484
        shape = self.paradict['shape']
        distances = 1 / (np.array(self.paradict['shape']) *
                         np.array(self.distances))
485
        datamodel = self.datamodel
486
        fft_module = self.fft_machine.name
487
        comm = self.comm
488
        complexity = {0: 1, 1: 0, 2: 2}[self.paradict['complexity']]
489
        harmonic = bool(not self.harmonic)
Marco Selig's avatar
Marco Selig committed
490

491
        new_space = rg_space(shape,
492
493
                             zerocenter=cozerocenter,
                             complexity=complexity,
494
                             distances=distances,
495
                             harmonic=harmonic,
496
                             datamodel=datamodel,
497
                             fft_module=fft_module,
498
                             comm=comm)
499
        return new_space
Marco Selig's avatar
Marco Selig committed
500

501
    def get_random_values(self, **kwargs):
Marco Selig's avatar
Marco Selig committed
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
        """
            Generates random field values according to the specifications given
            by the parameters, taking into account possible complex-valuedness
            and hermitian symmetry.

            Returns
            -------
            x : numpy.ndarray
                Valid field values.

            Other parameters
            ----------------
            random : string, *optional*
                Specifies the probability distribution from which the random
                numbers are to be drawn.
                Supported distributions are:

                - "pm1" (uniform distribution over {+1,-1} or {+1,+i,-1,-i}
520
521
                - "gau" (normal distribution with zero-mean and a given
                    standard
Marco Selig's avatar
Marco Selig committed
522
523
524
525
526
527
528
529
530
531
                    deviation or variance)
                - "syn" (synthesizes from a given power spectrum)
                - "uni" (uniform distribution over [vmin,vmax[)

                (default: None).
            dev : float, *optional*
                Standard deviation (default: 1).
            var : float, *optional*
                Variance, overriding `dev` if both are specified
                (default: 1).
532
533
            spec : {scalar, list, numpy.ndarray, nifty.field, function},
                *optional*
Marco Selig's avatar
Marco Selig committed
534
535
536
537
538
539
540
                Power spectrum (default: 1).
            pindex : numpy.ndarray, *optional*
                Indexing array giving the power spectrum index of each band
                (default: None).
            kindex : numpy.ndarray, *optional*
                Scale of each band (default: None).
            codomain : nifty.rg_space, *optional*
Ultimanet's avatar
Ultimanet committed
541
                A compatible codomain (default: None).
Marco Selig's avatar
Marco Selig committed
542
            log : bool, *optional*
543
544
                Flag specifying if the spectral binning is performed on
                    logarithmic
Marco Selig's avatar
Marco Selig committed
545
546
547
548
                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*
549
550
                Number of used spectral bins; if given `log` is set to
                    ``False``;
Marco Selig's avatar
Marco Selig committed
551
552
553
554
555
                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
556
                (default: None).
Ultimanet's avatar
Ultimanet committed
557
            vmin : float, *optional*
Marco Selig's avatar
Marco Selig committed
558
559
560
561
                Lower limit for a uniform distribution (default: 0).
            vmax : float, *optional*
                Upper limit for a uniform distribution (default: 1).
        """
562
        # Parse the keyword arguments
563
        arg = random.parse_arguments(self, **kwargs)
564

565
566
567
        if arg is None:
            return self.cast(0)

Ultima's avatar
Ultima committed
568
569
        # Should the output be hermitianized?
        hermitianizeQ = (self.paradict['complexity'] == 1)
Ultimanet's avatar
Ultimanet committed
570

571
        # Case 1: uniform distribution over {-1,+1}/{1,i,-1,-i}
Ultima's avatar
Ultima committed
572
573
        if arg['random'] == 'pm1' and not hermitianizeQ:
            sample = super(rg_space, self).get_random_values(**arg)
574

Ultima's avatar
Ultima committed
575
        elif arg['random'] == 'pm1' and hermitianizeQ:
576
            sample = self.get_random_values(random='uni', vmin=-1, vmax=1)
Ultima's avatar
Ultima committed
577

578
            if issubclass(sample.dtype.type, np.complexfloating):
Ultima's avatar
Ultima committed
579
580
581
582
583
                temp_data = sample.copy()
                sample[temp_data.real >= 0.5] = 1
                sample[(temp_data.real >= 0) * (temp_data.real < 0.5)] = -1
                sample[(temp_data.real < 0) * (temp_data.imag >= 0)] = 1j
                sample[(temp_data.real < 0) * (temp_data.imag < 0)] = -1j
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
                # Set the mirroring invariant points to real values
                product_list = []
                for s in self.get_shape():
                    # if the particular dimension has even length, set
                    # also the middle of the array to a real value
                    if s % 2 == 0:
                        product_list += [[0, s/2]]
                    else:
                        product_list += [[0]]

                for i in itertools.product(*product_list):
                    sample[i] = {1: 1,
                                 -1: -1,
                                 1j: 1,
                                 -1j: -1}[sample[i]]
Ultimanet's avatar
Ultimanet committed
599
            else:
Ultima's avatar
Ultima committed
600
601
                sample[sample >= 0] = 1
                sample[sample < 0] = -1
602

Ultima's avatar
Ultima committed
603
604
605
606
607
            try:
                sample.hermitian = True
            except(AttributeError):
                pass

608
        # Case 2: normal distribution with zero-mean and a given standard
609
        #         deviation or variance
Ultima's avatar
Ultima committed
610
611
        elif arg['random'] == 'gau':
            sample = super(rg_space, self).get_random_values(**arg)
612

613
            if hermitianizeQ:
Ultima's avatar
Ultima committed
614
                sample = utilities.hermitianize_gaussian(sample)
Ultimanet's avatar
Ultimanet committed
615

616
        # Case 3: uniform distribution
Ultima's avatar
Ultima committed
617
618
        elif arg['random'] == "uni" and not hermitianizeQ:
            sample = super(rg_space, self).get_random_values(**arg)
619

Ultima's avatar
Ultima committed
620
        elif arg['random'] == "uni" and hermitianizeQ:
621
622
623
624
625
            # For a hermitian uniform sample, generate a gaussian one
            # and then convert it to a uniform one
            sample = self.get_random_values(random='gau')
            # Use the cummulative of the gaussian, the error function in order
            # to transform it to a uniform distribution.
626
            if issubclass(sample.dtype.type, np.complexfloating):
Ultima's avatar
Ultima committed
627
                def temp_erf(x):
628
                    return erf(x.real) + 1j * erf(x.imag)
Ultimanet's avatar
Ultimanet committed
629
            else:
Ultima's avatar
Ultima committed
630
                def temp_erf(x):
631
                    return erf(x / np.sqrt(2))
Ultima's avatar
Ultima committed
632

633
            sample.apply_scalar_function(function=temp_erf, inplace=True)
634
635

            # Shift and stretch the uniform distribution into the given limits
636
            # sample = (sample + 1)/2 * (vmax-vmin) + vmin
Ultima's avatar
Ultima committed
637
638
            vmin = arg['vmin']
            vmax = arg['vmax']
639
640
            sample *= (vmax - vmin) / 2.
            sample += 1 / 2. * (vmax + vmin)
Marco Selig's avatar
Marco Selig committed
641

Ultima's avatar
Ultima committed
642
643
644
645
646
            try:
                sample.hermitian = True
            except(AttributeError):
                pass

Ultima's avatar
Ultima committed
647
648
649
650
        elif(arg['random'] == "syn"):
            spec = arg['spec']
            kpack = arg['kpack']
            harmonic_domain = arg['harmonic_domain']
Ultima's avatar
Ultima committed
651
652
653
654
655
            lnb_dict = {}
            for name in ('log', 'nbin', 'binbounds'):
                if arg[name] != 'default':
                    lnb_dict[name] = arg[name]

656
657
658
            # Check whether there is a kpack available or not.
            # kpack is only used for computing kdict and extracting kindex
            # If not, take kdict and kindex from the fourier_domain
659
            if kpack is None:
Ultimanet's avatar
Ultimanet committed
660
                power_indices =\
Ultima's avatar
Ultima committed
661
                    harmonic_domain.power_indices.get_index_dict(**lnb_dict)
662

Ultimanet's avatar
Ultimanet committed
663
664
665
666
667
668
                kindex = power_indices['kindex']
                kdict = power_indices['kdict']
                kpack = [power_indices['pindex'], power_indices['kindex']]
            else:
                kindex = kpack[1]
                kdict = harmonic_domain.power_indices.\
669
670
671
672
673
674
675
676
                    _compute_kdict_from_pindex_kindex(kpack[0], kpack[1])

            # draw the random samples
            # Case 1: self is a harmonic space
            if self.harmonic:
                # subcase 1: self is real
                # -> simply generate a random field in fourier space and
                # weight the entries accordingly to the powerspectrum
Ultimanet's avatar
Ultimanet committed
677
                if self.paradict['complexity'] == 0:
Ultima's avatar
Ultima committed
678
679
680
                    sample = self.get_random_values(random='gau',
                                                    mean=0,
                                                    std=1)
681
682
683
684
685
                # subcase 2: self is hermitian but probably complex
                # -> generate a real field (in position space) and transform
                # it to harmonic space -> field in harmonic space is
                # hermitian. Now weight the modes accordingly to the
                # powerspectrum.
Ultimanet's avatar
Ultimanet committed
686
687
                elif self.paradict['complexity'] == 1:
                    temp_codomain = self.get_codomain()
Ultima's avatar
Ultima committed
688
689
690
                    sample = temp_codomain.get_random_values(random='gau',
                                                             mean=0,
                                                             std=1)
691
692
693
694
695
696

                    # In order to get the normalisation right, the sqrt
                    # of self.dim must be divided out.
                    # Furthermore, the normalisation in the fft routine
                    # must be undone
                    # TODO: Insert explanation
697
                    sqrt_of_dim = np.sqrt(self.get_dim())
Ultimanet's avatar
Ultimanet committed
698
699
700
                    sample /= sqrt_of_dim
                    sample = temp_codomain.calc_weight(sample, power=-1)

701
                    # tronsform the random field to harmonic space
Ultimanet's avatar
Ultimanet committed
702
                    sample = temp_codomain.\
703
704
705
706
                        calc_transform(sample, codomain=self)

                    # ensure that the kdict and the harmonic_sample have the
                    # same distribution strategy
Ultima's avatar
Ultima committed
707
708
709
710
711
                    try:
                        assert(kdict.distribution_strategy ==
                               sample.distribution_strategy)
                    except AttributeError:
                        pass
712
713
714
715

                # subcase 3: self is fully complex
                # -> generate a complex random field in harmonic space and
                # weight the modes accordingly to the powerspectrum
Ultimanet's avatar
Ultimanet committed
716
                elif self.paradict['complexity'] == 2:
Ultima's avatar
Ultima committed
717
718
719
                    sample = self.get_random_values(random='gau',
                                                    mean=0,
                                                    std=1)
720

721
                # apply the powerspectrum renormalization
722
723
724
725
726
727
728
                # extract the local data from kdict
                local_kdict = kdict.get_local_data()
                rescaler = np.sqrt(
                    spec[np.searchsorted(kindex, local_kdict)])
                sample.apply_scalar_function(lambda x: x * rescaler,
                                             inplace=True)

729
            # Case 2: self is a position space
Ultimanet's avatar
Ultimanet committed
730
            else:
731
732
                # get a suitable codomain
                temp_codomain = self.get_codomain()
Ultimanet's avatar
Ultimanet committed
733

734
735
736
                # subcase 1: self is a real space.
                # -> generate a hermitian sample with the codomain in harmonic
                # space and make a fourier transformation.
Ultimanet's avatar
Ultimanet committed
737
                if self.paradict['complexity'] == 0:
738
                    # check that the codomain is hermitian
Ultimanet's avatar
Ultimanet committed
739
                    assert(temp_codomain.paradict['complexity'] == 1)
740
741
742
743

                # subcase 2: self is hermitian but probably complex
                # -> generate a real-valued random sample in fourier space
                # and transform it to real space
Ultimanet's avatar
Ultimanet committed
744
                elif self.paradict['complexity'] == 1:
745
746
                    # check that the codomain is real
                    assert(temp_codomain.paradict['complexity'] == 0)
Ultimanet's avatar
Ultimanet committed
747

748
749
750
751
752
753
                # subcase 3: self is fully complex
                # -> generate a complex-valued random sample in fourier space
                # and transform it to real space
                elif self.paradict['complexity'] == 2:
                    # check that the codomain is real
                    assert(temp_codomain.paradict['complexity'] == 2)
Ultimanet's avatar
Ultimanet committed
754

755
756
                # Get a hermitian/real/complex sample in harmonic space from
                # the codomain
Ultima's avatar
Ultima committed
757
758
759
760
761
                sample = temp_codomain.get_random_values(random='syn',
                                                         pindex=kpack[0],
                                                         kindex=kpack[1],
                                                         spec=spec,
                                                         codomain=self,
Ultima's avatar
Ultima committed
762
                                                         **lnb_dict)
763

764
                # Perform a fourier transform
Ultima's avatar
Ultima committed
765
                sample = temp_codomain.calc_transform(sample, codomain=self)
Ultimanet's avatar
Ultimanet committed
766
767

            if self.paradict['complexity'] == 1:
Ultima's avatar
Ultima committed
768
769
770
771
                try:
                    sample.hermitian = True
                except AttributeError:
                    pass
772

Ultimanet's avatar
Ultimanet committed
773
774
        else:
            raise KeyError(about._errors.cstring(
Ultima's avatar
Ultima committed
775
                "ERROR: unsupported random key '" + str(arg['random']) + "'."))
Marco Selig's avatar
Marco Selig committed
776

777
        return sample
Marco Selig's avatar
Marco Selig committed
778

Ultimanet's avatar
Ultimanet committed
779
    def calc_weight(self, x, power=1):
Marco Selig's avatar
Marco Selig committed
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
        """
            Weights a given array with the pixel 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.
        """
795
796
        # weight
        x = x * self.get_weight(power=power)
Ultimanet's avatar
Ultimanet committed
797
        return x
Marco Selig's avatar
Marco Selig committed
798

799
    def get_weight(self, power=1):
800
        return np.prod(self.distances)**power
801

802
    def calc_dot(self, x, y):
Marco Selig's avatar
Marco Selig committed
803
        """
804
805
            Computes the discrete inner product of two given arrays of field
            values.
Marco Selig's avatar
Marco Selig committed
806
807
808
809
810
811
812
813
814
815
816
817
818

            Parameters
            ----------
            x : numpy.ndarray
                First array
            y : numpy.ndarray
                Second array

            Returns
            -------
            dot : scalar
                Inner product of the two arrays.
        """
819
820
        x = self.cast(x)
        y = self.cast(y)
821

822
        result = x.vdot(y)
823

824
        if np.isreal(result):
825
            result = np.asscalar(np.real(result))
Ultimanet's avatar
Ultimanet committed
826
        if self.paradict['complexity'] != 2:
827
828
            if (np.absolute(result.imag) >
                    self.epsilon**2 * np.absolute(result.real)):
Ultimanet's avatar
Ultimanet committed
829
830
                about.warnings.cprint(
                    "WARNING: Discarding considerable imaginary part.")
831
            result = np.asscalar(np.real(result))
832
        return result
Marco Selig's avatar
Marco Selig committed
833

834
    def calc_transform(self, x, codomain=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
835
836
837
838
839
840
841
842
        """
            Computes the transform of a given array of field values.

            Parameters
            ----------
            x : numpy.ndarray
                Array to be transformed.
            codomain : nifty.rg_space, *optional*
843
                codomain space to which the transformation shall map
Marco Selig's avatar
Marco Selig committed
844
845
846
847
848
849
850
                (default: None).

            Returns
            -------
            Tx : numpy.ndarray
                Transformed array
        """
851
        x = self.cast(x)
852

853
        if codomain is None:
Ultimanet's avatar
Ultimanet committed
854
            codomain = self.get_codomain()
855
856

        # Check if the given codomain is suitable for the transformation
857
        if not self.check_codomain(codomain):
858
            raise ValueError(about._errors.cstring(
859
                "ERROR: unsupported codomain."))
860

861
        if codomain.harmonic:
862
            # correct for forward fft
863
            x = self.calc_weight(x, power=1)
864
865
866

        # Perform the transformation
        Tx = self.fft_machine.transform(val=x, domain=self, codomain=codomain,
867
868
                                        **kwargs)

869
        if not codomain.harmonic:
870
            # correct for inverse fft
Ultimanet's avatar
Ultimanet committed
871
872
            Tx = codomain.calc_weight(Tx, power=-1)

873
874
875
        # when the codomain space is purely real, the result of the
        # transformation must be corrected accordingly. Using the casting
        # method of codomain is sufficient
876
        # TODO: Let .transform  yield the correct dtype
877
        Tx = codomain.cast(Tx)
878

879
880
        return Tx

Ultimanet's avatar
Ultimanet committed
881
    def calc_smooth(self, x, sigma=0, codomain=None):
Marco Selig's avatar
Marco Selig committed
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
        """
            Smoothes an array of field values by convolution with a Gaussian
            kernel.

            Parameters
            ----------
            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; for testing: a sigma of -1 will be
                reset to a reasonable value (default: 0).

            Returns
            -------
            Gx : numpy.ndarray
                Smoothed array.
        """

901
        # Check sigma
Ultimanet's avatar
Ultimanet committed
902
        if sigma == 0:
Ultima's avatar
Ultima committed
903
            return self.unary_operation(x, op='copy')
Ultimanet's avatar
Ultimanet committed
904
905
906
        elif sigma == -1:
            about.infos.cprint(
                "INFO: Resetting sigma to sqrt(2)*max(dist).")
907
            sigma = np.sqrt(2) * np.max(self.distances)
908
        elif(sigma < 0):
Marco Selig's avatar
Marco Selig committed
909
            raise ValueError(about._errors.cstring("ERROR: invalid sigma."))
Ultimanet's avatar
Ultimanet committed
910

911
        # if a codomain was given...
912
        if codomain is not None:
913
            # ...check if it was suitable
Ultimanet's avatar
Ultimanet committed
914
915
            if not self.check_codomain(codomain):
                raise ValueError(about._errors.cstring(
916
917
                    "ERROR: the given codomain is not a compatible!"))
        else:
Ultimanet's avatar
Ultimanet committed
918
919
            codomain = self.get_codomain()

920
921
922
923
        x = self.calc_transform(x, codomain=codomain)
        x = codomain._calc_smooth_helper(x, sigma)
        x = codomain.calc_transform(x, codomain=self)
        return x
924

925
926
    def _calc_smooth_helper(self, x, sigma):
        # multiply the gaussian kernel, etc...
927
928
929
930
931
932

        # Cast the input
        x = self.cast(x)

        # if x is hermitian it remains hermitian during smoothing
        if self.datamodel in RG_DISTRIBUTION_STRATEGIES:
933
            remeber_hermitianQ = x.hermitian
Ultimanet's avatar
Ultimanet committed
934

935
936
937
938
        # Define the Gaussian kernel function
        gaussian = lambda x: np.exp(-2. * np.pi**2 * x**2 * sigma**2)

        # Define the variables in the dialect of the legacy smoothing.py
939
940
        nx = np.array(self.get_shape())
        dx = 1 / nx / self.distances
941
        # Multiply the data along each axis with suitable the gaussian kernel
Ultimanet's avatar
Ultimanet committed
942
        for i in range(len(nx)):
943
944
            # Prepare the exponent
            dk = 1. / nx[i] / dx[i]
Ultimanet's avatar
Ultimanet committed
945
            nk = nx[i]
946
            k = -0.5 * nk * dk + np.arange(nk) * dk
Ultimanet's avatar
Ultimanet committed
947
948
            if self.paradict['zerocenter'][i] == False:
                k = np.fft.fftshift(k)
949
            # compute the actual kernel vector
Ultimanet's avatar
Ultimanet committed
950
            gaussian_kernel_vector = gaussian(k)
951
952
            # blow up the vector to an array of shape (1,.,1,len(nk),1,.,1)
            blown_up_shape = [1, ] * len(nx)
Ultimanet's avatar
Ultimanet committed
953
954
955
            blown_up_shape[i] = len(gaussian_kernel_vector)
            gaussian_kernel_vector =\
                gaussian_kernel_vector.reshape(blown_up_shape)
956
957
            # apply the blown-up gaussian_kernel_vector
            x = x*gaussian_kernel_vector
958

959
        try:
960
            x.hermitian = remeber_hermitianQ
961
962
        except AttributeError:
            pass
963

Ultimanet's avatar
Ultimanet committed
964
        return x
Marco Selig's avatar
Marco Selig committed
965

966
    def calc_power(self, x, **kwargs):
Marco Selig's avatar
Marco Selig committed
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
        """
            Computes the power of an array of field values.

            Parameters
            ----------
            x : numpy.ndarray
                Array containing the field values of which the power is to be
                calculated.

            Returns
            -------
            spec : numpy.ndarray
                Power contained in the input array.

            Other parameters
            ----------------
            pindex : numpy.ndarray, *optional*
                Indexing array assigning the input array components to
                components of the power spectrum (default: None).
            rho : numpy.ndarray, *optional*
                Number of degrees of freedom per band (default: None).
            codomain : nifty.space, *optional*
                A compatible codomain for power indexing (default: None).
            log : bool, *optional*
991
992
                Flag specifying if the spectral binning is performed on
                logarithmic
Marco Selig's avatar
Marco Selig committed
993
994
995
996
                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*
997
998
                Number of used spectral bins; if given `log` is set to
                ``False``;
Marco Selig's avatar
Marco Selig committed
999
1000
1001
1002
1003
                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
1004
                (default: None).
Marco Selig's avatar
Marco Selig committed
1005
1006

        """
Ultimanet's avatar
Ultimanet committed
1007
1008
        x = self.cast(x)

1009
        # If self is a position space, delegate calc_power to its codomain.
1010
        if not self.harmonic:
Marco Selig's avatar
Marco Selig committed
1011
            try:
1012
                codomain = kwargs['codomain']
Ultimanet's avatar
Ultimanet committed
1013
1014
            except(KeyError):
                codomain = self.get_codomain()
1015

Ultimanet's avatar
Ultimanet committed
1016
1017
1018
            y = self.calc_transform(x, codomain)
            kwargs.update({'codomain': self})
            return codomain.calc_power(y, **kwargs)
1019
1020
1021
1022
1023

        # If some of the pindex, kindex or rho arrays are given explicitly,
        # favor them over those from the self.power_indices dictionary.
        # As the default value in kwargs.get(key, default) does NOT evaluate
        # lazy, a distinction of cases is necessary. Otherwise the
Ultima's avatar
Ultima committed
1024
1025
        # powerindices might be computed, although not needed
        if 'pindex' in kwargs and 'rho' in kwargs:
Ultimanet's avatar
Ultimanet committed
1026
1027
1028
            pindex = kwargs.get('pindex')
            rho = kwargs.get('rho')
        else:
Ultima's avatar
Ultima committed
1029
            power_indices = self.power_indices.get_index_dict(**kwargs)
Ultimanet's avatar
Ultimanet committed
1030
1031
            pindex = kwargs.get('pindex', power_indices['pindex'])
            rho = kwargs.get('rho', power_indices['rho'])
1032

Ultimanet's avatar
Ultimanet committed
1033
        fieldabs = abs(x)**2
1034
        power_spectrum = np.zeros(rho.shape)
1035

1036
        power_spectrum = pindex.bincount(weights=fieldabs)
1037
1038

        # Divide out the degeneracy factor
Ultimanet's avatar
Ultimanet committed
1039
1040
        power_spectrum /= rho
        return power_spectrum