field.py 45.9 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# NIFTy
# Copyright (C) 2017  Theo Steininger
#
# Author: Theo Steininger
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

csongor's avatar
csongor committed
19
from __future__ import division
20
21

import itertools
csongor's avatar
csongor committed
22
23
import numpy as np

Theo Steininger's avatar
Theo Steininger committed
24
25
from keepers import Versionable,\
                    Loggable
Jait Dixit's avatar
Jait Dixit committed
26

27
from d2o import distributed_data_object,\
28
    STRATEGIES as DISTRIBUTION_STRATEGIES
csongor's avatar
csongor committed
29

30
from nifty.config import nifty_configuration as gc
csongor's avatar
csongor committed
31

32
from nifty.domain_object import DomainObject
33

34
from nifty.spaces.power_space import PowerSpace
csongor's avatar
csongor committed
35

csongor's avatar
csongor committed
36
import nifty.nifty_utilities as utilities
37
38
from nifty.random import Random

csongor's avatar
csongor committed
39

Jait Dixit's avatar
Jait Dixit committed
40
class Field(Loggable, Versionable, object):
Theo Steininger's avatar
Theo Steininger committed
41
42
43
    """ The discrete representation of a continuous field over multiple spaces.

    In NIFTY, Fields are used to store data arrays and carry all the needed
44
    metainformation (i.e. the domain) for operators to be able to work on them.
Theo Steininger's avatar
Theo Steininger committed
45
46
    In addition Field has methods to work with power-spectra.

47
48
49
50
    Parameters
    ----------
    domain : DomainObject
        One of the space types NIFTY supports. RGSpace, GLSpace, HPSpace,
Theo Steininger's avatar
Theo Steininger committed
51
        LMSpace or PowerSpace. It might also be a FieldArray, which is
52
        an unstructured domain.
Theo Steininger's avatar
Theo Steininger committed
53

54
55
56
57
    val : scalar, numpy.ndarray, distributed_data_object, Field
        The values the array should contain after init. A scalar input will
        fill the whole array with this scalar. If an array is provided the
        array's dimensions must match the domain's.
Theo Steininger's avatar
Theo Steininger committed
58

59
60
    dtype : type
        A numpy.type. Most common are int, float and complex.
Theo Steininger's avatar
Theo Steininger committed
61

62
63
64
65
66
67
    distribution_strategy: optional[{'fftw', 'equal', 'not', 'freeform'}]
        Specifies which distributor will be created and used.
        'fftw'      uses the distribution strategy of pyfftw,
        'equal'     tries to  distribute the data as uniform as possible
        'not'       does not distribute the data at all
        'freeform'  distribute the data according to the given local data/shape
Theo Steininger's avatar
Theo Steininger committed
68

69
70
71
72
73
    copy: boolean

    Attributes
    ----------
    val : distributed_data_object
Theo Steininger's avatar
Theo Steininger committed
74

75
76
77
78
79
80
81
    domain : DomainObject
        See Parameters.
    domain_axes : tuple of tuples
        Enumerates the axes of the Field
    dtype : type
        Contains the datatype stored in the Field.
    distribution_strategy : string
Theo Steininger's avatar
Theo Steininger committed
82
83
        Name of the used distribution_strategy.

84
85
86
87
88
89
90
    Raise
    -----
    TypeError
        Raised if
            *the given domain contains something that is not a DomainObject
             instance
            *val is an array that has a different dimension than the domain
Theo Steininger's avatar
Theo Steininger committed
91

92
93
94
95
96
97
98
99
100
101
102
    Examples
    --------
    >>> a = Field(RGSpace([4,5]),val=2)
    >>> a.val
    <distributed_data_object>
    array([[2, 2, 2, 2, 2],
           [2, 2, 2, 2, 2],
           [2, 2, 2, 2, 2],
           [2, 2, 2, 2, 2]])
    >>> a.dtype
    dtype('int64')
Theo Steininger's avatar
Theo Steininger committed
103

104
105
106
107
108
    See Also
    --------
    distributed_data_object

    """
109

Theo Steininger's avatar
Theo Steininger committed
110
    # ---Initialization methods---
111

112
    def __init__(self, domain=None, val=None, dtype=None,
113
                 distribution_strategy=None, copy=False):
csongor's avatar
csongor committed
114

115
        self.domain = self._parse_domain(domain=domain, val=val)
116
        self.domain_axes = self._get_axes_tuple(self.domain)
csongor's avatar
csongor committed
117

Theo Steininger's avatar
Theo Steininger committed
118
        self.dtype = self._infer_dtype(dtype=dtype,
119
                                       val=val)
120

121
122
123
        self.distribution_strategy = self._parse_distribution_strategy(
                                distribution_strategy=distribution_strategy,
                                val=val)
csongor's avatar
csongor committed
124

125
126
127
128
        if val is None:
            self._val = None
        else:
            self.set_val(new_val=val, copy=copy)
csongor's avatar
csongor committed
129

130
    def _parse_domain(self, domain, val=None):
131
        if domain is None:
132
133
134
135
            if isinstance(val, Field):
                domain = val.domain
            else:
                domain = ()
136
        elif isinstance(domain, DomainObject):
137
            domain = (domain,)
138
139
140
        elif not isinstance(domain, tuple):
            domain = tuple(domain)

csongor's avatar
csongor committed
141
        for d in domain:
142
            if not isinstance(d, DomainObject):
143
144
                raise TypeError(
                    "Given domain contains something that is not a "
145
                    "DomainObject instance.")
csongor's avatar
csongor committed
146
147
        return domain

Theo Steininger's avatar
Theo Steininger committed
148
149
150
151
152
153
154
155
156
157
    def _get_axes_tuple(self, things_with_shape, start=0):
        i = start
        axes_list = []
        for thing in things_with_shape:
            l = []
            for j in range(len(thing.shape)):
                l += [i]
                i += 1
            axes_list += [tuple(l)]
        return tuple(axes_list)
158

159
    def _infer_dtype(self, dtype, val):
csongor's avatar
csongor committed
160
        if dtype is None:
161
            try:
162
                dtype = val.dtype
163
            except AttributeError:
Theo Steininger's avatar
Theo Steininger committed
164
165
166
                try:
                    if val is None:
                        raise TypeError
167
                    dtype = np.result_type(val)
Theo Steininger's avatar
Theo Steininger committed
168
                except(TypeError):
169
                    dtype = np.dtype(gc['default_field_dtype'])
Theo Steininger's avatar
Theo Steininger committed
170
        else:
171
            dtype = np.dtype(dtype)
172

Theo Steininger's avatar
Theo Steininger committed
173
        return dtype
174

175
176
    def _parse_distribution_strategy(self, distribution_strategy, val):
        if distribution_strategy is None:
177
            if isinstance(val, distributed_data_object):
178
                distribution_strategy = val.distribution_strategy
179
            elif isinstance(val, Field):
180
                distribution_strategy = val.distribution_strategy
181
            else:
182
                self.logger.debug("distribution_strategy set to default!")
183
                distribution_strategy = gc['default_distribution_strategy']
184
        elif distribution_strategy not in DISTRIBUTION_STRATEGIES['global']:
185
186
187
            raise ValueError(
                    "distribution_strategy must be a global-type "
                    "strategy.")
188
        return distribution_strategy
189
190

    # ---Factory methods---
191

192
    @classmethod
193
    def from_random(cls, random_type, domain=None, dtype=None,
194
                    distribution_strategy=None, **kwargs):
195
196
197
198
199
        """ Draws a random field with the given parameters.

        Parameters
        ----------
        cls : class
Theo Steininger's avatar
Theo Steininger committed
200

201
202
203
        random_type : String
            'pm1', 'normal', 'uniform' are the supported arguments for this
            method.
Theo Steininger's avatar
Theo Steininger committed
204

205
206
        domain : DomainObject
            The domain of the output random field
Theo Steininger's avatar
Theo Steininger committed
207

208
209
        dtype : type
            The datatype of the output random field
Theo Steininger's avatar
Theo Steininger committed
210

211
212
        distribution_strategy : all supported distribution strategies
            The distribution strategy of the output random field
Theo Steininger's avatar
Theo Steininger committed
213

214
215
216
217
218
219
220
        Returns
        -------
        out : Field
            The output object.

        See Also
        --------
221
        power_synthesize
Theo Steininger's avatar
Theo Steininger committed
222

223
224

        """
Theo Steininger's avatar
Theo Steininger committed
225

226
        # create a initially empty field
227
        f = cls(domain=domain, dtype=dtype,
228
                distribution_strategy=distribution_strategy)
229
230
231
232
233
234
235

        # now use the processed input in terms of f in order to parse the
        # random arguments
        random_arguments = cls._parse_random_arguments(random_type=random_type,
                                                       f=f,
                                                       **kwargs)

Martin Reinecke's avatar
Martin Reinecke committed
236
        # extract the distributed_data_object from f and apply the appropriate
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
        # random number generator to it
        sample = f.get_val(copy=False)
        generator_function = getattr(Random, random_type)
        sample.apply_generator(
            lambda shape: generator_function(dtype=f.dtype,
                                             shape=shape,
                                             **random_arguments))
        return f

    @staticmethod
    def _parse_random_arguments(random_type, f, **kwargs):
        if random_type == "pm1":
            random_arguments = {}

        elif random_type == "normal":
            mean = kwargs.get('mean', 0)
            std = kwargs.get('std', 1)
            random_arguments = {'mean': mean,
                                'std': std}

        elif random_type == "uniform":
            low = kwargs.get('low', 0)
            high = kwargs.get('high', 1)
            random_arguments = {'low': low,
                                'high': high}

csongor's avatar
csongor committed
263
        else:
264
265
            raise KeyError(
                "unsupported random key '" + str(random_type) + "'.")
csongor's avatar
csongor committed
266

267
        return random_arguments
csongor's avatar
csongor committed
268

269
270
    # ---Powerspectral methods---

Theo Steininger's avatar
Theo Steininger committed
271
272
    def power_analyze(self, spaces=None, logarithmic=False, nbin=None,
                      binbounds=None, decompose_power=True):
273
        """ Computes the square root power spectrum for a subspace of the Field.
Theo Steininger's avatar
Theo Steininger committed
274

Theo Steininger's avatar
Theo Steininger committed
275
276
277
        Creates a PowerSpace for the space addressed by `spaces` with the given
        binning and computes the power spectrum as a Field over this
        PowerSpace. This can only be done if the subspace to  be analyzed is a
278
279
        harmonic space. The resulting field has the same units as the initial
		field, corresponding to the square root of the power spectrum.
280
281
282

        Parameters
        ----------
Theo Steininger's avatar
Theo Steininger committed
283
284
285
286
287
288
        spaces : int *optional*
            The subspace for which the powerspectrum shall be computed
            (default : None).
            if spaces==None : Tries to synthesize for the whole domain
        logarithmic : boolean *optional*
            True if the output PowerSpace should use logarithmic binning.
289
            {default : False}
Theo Steininger's avatar
Theo Steininger committed
290
291
292
293
294
295
296
297
298
299
300
301
        nbin : int *optional*
            The number of bins the resulting PowerSpace shall have
            (default : None).
            if nbin==None : maximum number of bins is used
        binbounds : array-like *optional*
            Inner bounds of the bins (default : None).
            if binbounds==None : bins are inferred. Overwrites nbins and log
        decompose_power : boolean, *optional*
            Whether the analysed signal-space Field is intrinsically real or
            complex and if the power spectrum shall therefore be computed
            for the real and the imaginary part of the Field separately
            (default : True).
Theo Steininger's avatar
Theo Steininger committed
302

303
304
305
306
        Raise
        -----
        ValueError
            Raised if
Theo Steininger's avatar
Theo Steininger committed
307
308
                *len(domain) is != 1 when spaces==None
                *len(spaces) is != 1 if not None
309
                *the analyzed space is not harmonic
Theo Steininger's avatar
Theo Steininger committed
310

311
312
        Returns
        -------
Theo Steininger's avatar
Theo Steininger committed
313
        out : Field
314
315
316
317
318
319
            The output object. It's domain is a PowerSpace and it contains
            the power spectrum of 'self's field.

        See Also
        --------
        power_synthesize, PowerSpace
Theo Steininger's avatar
Theo Steininger committed
320

321
        """
Theo Steininger's avatar
Theo Steininger committed
322

Theo Steininger's avatar
Theo Steininger committed
323
        # check if all spaces in `self.domain` are either harmonic or
324
325
326
        # power_space instances
        for sp in self.domain:
            if not sp.harmonic and not isinstance(sp, PowerSpace):
Theo Steininger's avatar
Theo Steininger committed
327
                self.logger.info(
328
                    "Field has a space in `domain` which is neither "
329
330
331
                    "harmonic nor a PowerSpace.")

        # check if the `spaces` input is valid
332
333
334
335
336
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
        if spaces is None:
            if len(self.domain) == 1:
                spaces = (0,)
            else:
337
338
339
                raise ValueError(
                    "Field has multiple spaces as domain "
                    "but `spaces` is None.")
340
341

        if len(spaces) == 0:
342
343
            raise ValueError(
                "No space for analysis specified.")
344
        elif len(spaces) > 1:
345
346
            raise ValueError(
                "Conversion of only one space at a time is allowed.")
347
348
349
350

        space_index = spaces[0]

        if not self.domain[space_index].harmonic:
351
352
            raise ValueError(
                "The analyzed space must be harmonic.")
353

354
355
356
357
358
359
        # Create the target PowerSpace instance:
        # If the associated signal-space field was real, we extract the
        # hermitian and anti-hermitian parts of `self` and put them
        # into the real and imaginary parts of the power spectrum.
        # If it was complex, all the power is put into a real power spectrum.

360
361
362
363
        distribution_strategy = \
            self.val.get_axes_local_distribution_strategy(
                self.domain_axes[space_index])

364
        harmonic_domain = self.domain[space_index]
365
        power_domain = PowerSpace(harmonic_partner=harmonic_domain,
366
                                  distribution_strategy=distribution_strategy,
Theo Steininger's avatar
Theo Steininger committed
367
368
                                  logarithmic=logarithmic, nbin=nbin,
                                  binbounds=binbounds)
369

370
        # extract pindex and rho from power_domain
371
372
        pindex = power_domain.pindex
        rho = power_domain.rho
373

Theo Steininger's avatar
Theo Steininger committed
374
        if decompose_power:
375
            hermitian_part, anti_hermitian_part = \
376
                harmonic_domain.hermitian_decomposition(
377
378
379
380
381
382
383
384
385
386
387
388
389
390
                                            self.val,
                                            axes=self.domain_axes[space_index])

            [hermitian_power, anti_hermitian_power] = \
                [self._calculate_power_spectrum(
                                            x=part,
                                            pindex=pindex,
                                            rho=rho,
                                            axes=self.domain_axes[space_index])
                 for part in [hermitian_part, anti_hermitian_part]]

            power_spectrum = hermitian_power + 1j * anti_hermitian_power
        else:
            power_spectrum = self._calculate_power_spectrum(
391
392
393
394
395
396
397
398
399
                                            x=self.val,
                                            pindex=pindex,
                                            rho=rho,
                                            axes=self.domain_axes[space_index])

        # create the result field and put power_spectrum into it
        result_domain = list(self.domain)
        result_domain[space_index] = power_domain

Theo Steininger's avatar
Theo Steininger committed
400
        if decompose_power:
401
402
403
404
            result_dtype = np.complex
        else:
            result_dtype = np.float

405
406
        result_field = self.copy_empty(
                   domain=result_domain,
407
                   dtype=result_dtype,
408
                   distribution_strategy=power_spectrum.distribution_strategy)
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
        result_field.set_val(new_val=power_spectrum, copy=False)

        return result_field

    def _calculate_power_spectrum(self, x, pindex, rho, axes=None):
        fieldabs = abs(x)
        fieldabs **= 2

        if axes is not None:
            pindex = self._shape_up_pindex(
                                    pindex=pindex,
                                    target_shape=x.shape,
                                    target_strategy=x.distribution_strategy,
                                    axes=axes)
        power_spectrum = pindex.bincount(weights=fieldabs,
                                         axis=axes)
        if axes is not None:
            new_rho_shape = [1, ] * len(power_spectrum.shape)
            new_rho_shape[axes[0]] = len(rho)
            rho = rho.reshape(new_rho_shape)
        power_spectrum /= rho

        power_spectrum **= 0.5
        return power_spectrum

    def _shape_up_pindex(self, pindex, target_shape, target_strategy, axes):
        if pindex.distribution_strategy not in \
                DISTRIBUTION_STRATEGIES['global']:
437
            raise ValueError("pindex's distribution strategy must be "
438
439
440
441
442
443
                             "global-type")

        if pindex.distribution_strategy in DISTRIBUTION_STRATEGIES['slicing']:
            if ((0 not in axes) or
                    (target_strategy is not pindex.distribution_strategy)):
                raise ValueError(
444
                    "A slicing distributor shall not be reshaped to "
445
446
447
448
449
450
451
452
453
454
455
456
457
                    "something non-sliced.")

        semiscaled_shape = [1, ] * len(target_shape)
        for i in axes:
            semiscaled_shape[i] = target_shape[i]
        local_data = pindex.get_local_data(copy=False)
        semiscaled_local_data = local_data.reshape(semiscaled_shape)
        result_obj = pindex.copy_empty(global_shape=target_shape,
                                       distribution_strategy=target_strategy)
        result_obj.set_full_data(semiscaled_local_data, copy=False)

        return result_obj

458
459
    def power_synthesize(self, spaces=None, real_power=True, real_signal=True,
                         mean=None, std=None):
460
        """Yields a sampled field with this field squared as its power spectrum.
Theo Steininger's avatar
Theo Steininger committed
461

462
463
        This method draws a Gaussian random field in the harmonic partner domain
        of this fields domains, using this field as power spectrum.
Theo Steininger's avatar
Theo Steininger committed
464

465
466
        Notes
        -----
467
468
469
        For this the spaces specified by `spaces` must be a PowerSpace.
		This expects this field to be the square root of a power spectrum, i.e. 
		to have the unit of the field to be sampled.
Theo Steininger's avatar
Theo Steininger committed
470

471
472
473
        Parameters
        ----------
        spaces : {tuple, int, None} *optional*
Theo Steininger's avatar
Theo Steininger committed
474
475
476
            Specifies the subspace containing all the PowerSpaces which
            should be converted (default : None).
            if spaces==None : Tries to convert the whole domain.
477
        real_power : boolean *optional*
Theo Steininger's avatar
Theo Steininger committed
478
479
            Determines whether the power spectrum is treated as intrinsically
            real or complex (default : True).
480
        real_signal : boolean *optional*
Theo Steininger's avatar
Theo Steininger committed
481
482
483
484
485
486
            True will result in a purely real signal-space field
            (default : True).
        mean : float *optional*
            The mean of the Gaussian noise field which is used for the Field
            synthetization (default : None).
            if mean==None : mean will be set to 0
487
        std : float *optional*
Theo Steininger's avatar
Theo Steininger committed
488
489
490
            The standard deviation of the Gaussian noise field which is used
            for the Field synthetization (default : None).
            if std==None : std will be set to 1
Theo Steininger's avatar
Theo Steininger committed
491

492
493
494
495
        Returns
        -------
        out : Field
            The output object. A random field created with the power spectrum
Theo Steininger's avatar
Theo Steininger committed
496
            stored in the `spaces` in `self`.
497
498
499
500

        See Also
        --------
        power_analyze
501
502
503
		Raises
		------
		ValueError : If domain is not a PowerSpace
504
        """
Theo Steininger's avatar
Theo Steininger committed
505

506
507
508
        # check if the `spaces` input is valid
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))

Theo Steininger's avatar
Theo Steininger committed
509
510
511
        if spaces is None:
            spaces = range(len(self.domain))

512
513
514
515
516
        for power_space_index in spaces:
            power_space = self.domain[power_space_index]
            if not isinstance(power_space, PowerSpace):
                raise ValueError("A PowerSpace is needed for field "
                                 "synthetization.")
517
518
519

        # create the result domain
        result_domain = list(self.domain)
520
521
        for power_space_index in spaces:
            power_space = self.domain[power_space_index]
522
            harmonic_domain = power_space.harmonic_partner
523
            result_domain[power_space_index] = harmonic_domain
524
525
526

        # create random samples: one or two, depending on whether the
        # power spectrum is real or complex
527
        if real_power:
528
            result_list = [None]
529
530
        else:
            result_list = [None, None]
531

532
533
        result_list = [self.__class__.from_random(
                             'normal',
534
535
536
                             mean=mean,
                             std=std,
                             domain=result_domain,
537
                             dtype=np.complex,
538
                             distribution_strategy=self.distribution_strategy)
539
540
541
542
543
544
                       for x in result_list]

        # from now on extract the values from the random fields for further
        # processing without killing the fields.
        # if the signal-space field should be real, hermitianize the field
        # components
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562

        spec = self.val.get_full_data()
        for power_space_index in spaces:
            spec = self._spec_to_rescaler(spec, result_list, power_space_index)
        local_rescaler = spec

        result_val_list = [x.val for x in result_list]

        # apply the rescaler to the random fields
        result_val_list[0].apply_scalar_function(
                                            lambda x: x * local_rescaler.real,
                                            inplace=True)

        if not real_power:
            result_val_list[1].apply_scalar_function(
                                            lambda x: x * local_rescaler.imag,
                                            inplace=True)

563
        if real_signal:
564
565
566
567
568
569
            result_val_list = [self._hermitian_decomposition(
                                                result_domain,
                                                result_val,
                                                spaces,
                                                result_list[0].domain_axes)[0]
                               for result_val in result_val_list]
570
571
572
573
574
575
576

        # store the result into the fields
        [x.set_val(new_val=y, copy=False) for x, y in
            zip(result_list, result_val_list)]

        if real_power:
            result = result_list[0]
577
        else:
578
579
580
581
            result = result_list[0] + 1j*result_list[1]

        return result

582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
    @staticmethod
    def _hermitian_decomposition(domain, val, spaces, domain_axes):
        # hermitianize for the first space
        (h, a) = domain[spaces[0]].hermitian_decomposition(
                                                       val,
                                                       domain_axes[spaces[0]])
        # hermitianize all remaining spaces using the iterative formula
        for space in xrange(1, len(spaces)):
            (hh, ha) = \
                domain[space].hermitian_decomposition(h, domain_axes[space])
            (ah, aa) = \
                domain[space].hermitian_decomposition(a, domain_axes[space])
            c = (hh - ha - ah + aa).conjugate()
            h = (val + c)/2.
            a = (val - c)/2.

        # correct variance
        fixed_points = [domain[i].hermitian_fixed_points() for i in spaces]
        # check if there was at least one flipping during hermitianization
        flipped_Q = np.any([fp is not None for fp in fixed_points])
        # if the array got flipped, correct the variance
        if flipped_Q:
            h *= np.sqrt(2)
            a *= np.sqrt(2)
            fixed_points = [[fp] if fp is None else fp for fp in fixed_points]
            for product_point in itertools.product(*fixed_points):
                slice_object = np.array((slice(None), )*len(val.shape),
                                        dtype=np.object)
                for i, sp in enumerate(spaces):
                    point_component = product_point[i]
                    if point_component is None:
                        point_component = slice(None)
                    slice_object[list(domain_axes[sp])] = point_component

                slice_object = tuple(slice_object)
                h[slice_object] /= np.sqrt(2)
                a[slice_object] /= np.sqrt(2)

        return (h, a)

622
623
    def _spec_to_rescaler(self, spec, result_list, power_space_index):
        power_space = self.domain[power_space_index]
624
625
626

        # weight the random fields with the power spectrum
        # therefore get the pindex from the power space
627
        pindex = power_space.pindex
628
629
630
631
632
633
634
        # take the local data from pindex. This data must be compatible to the
        # local data of the field given the slice of the PowerSpace
        local_distribution_strategy = \
            result_list[0].val.get_axes_local_distribution_strategy(
                result_list[0].domain_axes[power_space_index])

        if pindex.distribution_strategy is not local_distribution_strategy:
635
            self.logger.warn(
636
                "The distribution_stragey of pindex does not fit the "
637
638
639
640
641
642
643
644
645
646
                "slice_local distribution strategy of the synthesized field.")

        # Now use numpy advanced indexing in order to put the entries of the
        # power spectrum into the appropriate places of the pindex array.
        # Do this for every 'pindex-slice' in parallel using the 'slice(None)'s
        local_pindex = pindex.get_local_data(copy=False)

        local_blow_up = [slice(None)]*len(self.shape)
        local_blow_up[self.domain_axes[power_space_index][0]] = local_pindex
        # here, the power_spectrum is distributed into the new shape
647
648
        local_rescaler = spec[local_blow_up]
        return local_rescaler
649

Theo Steininger's avatar
Theo Steininger committed
650
    # ---Properties---
651

Theo Steininger's avatar
Theo Steininger committed
652
    def set_val(self, new_val=None, copy=False):
Theo Steininger's avatar
Theo Steininger committed
653
        """ Sets the fields distributed_data_object.
654
655
656

        Parameters
        ----------
Theo Steininger's avatar
Theo Steininger committed
657
        new_val : scalar, array-like, Field, None *optional*
658
659
            The values to be stored in the field.
            {default : None}
Theo Steininger's avatar
Theo Steininger committed
660

661
        copy : boolean, *optional*
Theo Steininger's avatar
Theo Steininger committed
662
663
            If False, Field tries to not copy the input data but use it
            directly.
664
665
666
667
668
669
            {default : False}
        See Also
        --------
        val

        """
Theo Steininger's avatar
Theo Steininger committed
670

671
672
        new_val = self.cast(new_val)
        if copy:
Theo Steininger's avatar
Theo Steininger committed
673
674
            new_val = new_val.copy()
        self._val = new_val
675
        return self
csongor's avatar
csongor committed
676

677
    def get_val(self, copy=False):
Theo Steininger's avatar
Theo Steininger committed
678
        """ Returns the distributed_data_object associated with this Field.
679
680
681
682

        Parameters
        ----------
        copy : boolean
Theo Steininger's avatar
Theo Steininger committed
683
684
            If true, a copy of the Field's underlying distributed_data_object
            is returned.
Theo Steininger's avatar
Theo Steininger committed
685

686
687
688
689
690
691
692
693
694
        Returns
        -------
        out : distributed_data_object

        See Also
        --------
        val

        """
Theo Steininger's avatar
Theo Steininger committed
695

696
697
698
        if self._val is None:
            self.set_val(None)

699
        if copy:
Theo Steininger's avatar
Theo Steininger committed
700
            return self._val.copy()
701
        else:
Theo Steininger's avatar
Theo Steininger committed
702
            return self._val
csongor's avatar
csongor committed
703

Theo Steininger's avatar
Theo Steininger committed
704
705
    @property
    def val(self):
Theo Steininger's avatar
Theo Steininger committed
706
        """ Returns the distributed_data_object associated with this Field.
Theo Steininger's avatar
Theo Steininger committed
707

708
709
710
711
712
713
714
715
716
        Returns
        -------
        out : distributed_data_object

        See Also
        --------
        get_val

        """
Theo Steininger's avatar
Theo Steininger committed
717

718
        return self.get_val(copy=False)
csongor's avatar
csongor committed
719

Theo Steininger's avatar
Theo Steininger committed
720
721
    @val.setter
    def val(self, new_val):
722
        self.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
723

724
725
    @property
    def shape(self):
Theo Steininger's avatar
Theo Steininger committed
726
        """ Returns the total shape of the Field's data array.
Theo Steininger's avatar
Theo Steininger committed
727

728
729
730
731
732
733
734
735
736
737
738
        Returns
        -------
        out : tuple
            The output object. The tuple contains the dimansions of the spaces
            in domain.

        See Also
        --------
        dim

        """
Theo Steininger's avatar
Theo Steininger committed
739

740
        shape_tuple = tuple(sp.shape for sp in self.domain)
741
742
743
744
        try:
            global_shape = reduce(lambda x, y: x + y, shape_tuple)
        except TypeError:
            global_shape = ()
csongor's avatar
csongor committed
745

746
        return global_shape
csongor's avatar
csongor committed
747

748
749
    @property
    def dim(self):
Theo Steininger's avatar
Theo Steininger committed
750
        """ Returns the total number of pixel-dimensions the field has.
Theo Steininger's avatar
Theo Steininger committed
751

Theo Steininger's avatar
Theo Steininger committed
752
        Effectively, all values from shape are multiplied.
Theo Steininger's avatar
Theo Steininger committed
753

754
755
756
757
758
759
760
761
762
763
        Returns
        -------
        out : int
            The dimension of the Field.

        See Also
        --------
        shape

        """
Theo Steininger's avatar
Theo Steininger committed
764

765
        dim_tuple = tuple(sp.dim for sp in self.domain)
Theo Steininger's avatar
Theo Steininger committed
766
767
768
769
        try:
            return reduce(lambda x, y: x * y, dim_tuple)
        except TypeError:
            return 0
csongor's avatar
csongor committed
770

771
772
    @property
    def dof(self):
Theo Steininger's avatar
Theo Steininger committed
773
774
775
776
777
778
        """ Returns the total number of degrees of freedom the Field has. For
        real Fields this is equal to `self.dim`. For complex Fields it is
        2*`self.dim`.

        """

Theo Steininger's avatar
Theo Steininger committed
779
780
781
782
783
784
785
        dof = self.dim
        if issubclass(self.dtype.type, np.complexfloating):
            dof *= 2
        return dof

    @property
    def total_volume(self):
Theo Steininger's avatar
Theo Steininger committed
786
787
788
        """ Returns the total volume of all spaces in the domain.
        """

Theo Steininger's avatar
Theo Steininger committed
789
        volume_tuple = tuple(sp.total_volume for sp in self.domain)
790
        try:
Theo Steininger's avatar
Theo Steininger committed
791
            return reduce(lambda x, y: x * y, volume_tuple)
792
        except TypeError:
Theo Steininger's avatar
Theo Steininger committed
793
            return 0.
794

Theo Steininger's avatar
Theo Steininger committed
795
    # ---Special unary/binary operations---
796

csongor's avatar
csongor committed
797
    def cast(self, x=None, dtype=None):
Theo Steininger's avatar
Theo Steininger committed
798
        """ Transforms x to a d2o with the correct dtype and shape.
Theo Steininger's avatar
Theo Steininger committed
799

800
801
        Parameters
        ----------
Theo Steininger's avatar
Theo Steininger committed
802
        x : scalar, d2o, Field, array_like
803
804
            The input that shall be casted on a d2o of the same shape like the
            domain.
Theo Steininger's avatar
Theo Steininger committed
805

806
        dtype : type
Theo Steininger's avatar
Theo Steininger committed
807
808
            The datatype the output shall have. This can be used to override
            the fields dtype.
Theo Steininger's avatar
Theo Steininger committed
809

810
811
812
813
814
815
816
817
818
819
        Returns
        -------
        out : distributed_data_object
            The output object.

        See Also
        --------
        _actual_cast

        """
csongor's avatar
csongor committed
820
821
        if dtype is None:
            dtype = self.dtype
822
823
        else:
            dtype = np.dtype(dtype)
824

825
826
        casted_x = x

827
        for ind, sp in enumerate(self.domain):
828
            casted_x = sp.pre_cast(casted_x,
829
830
831
                                   axes=self.domain_axes[ind])

        casted_x = self._actual_cast(casted_x, dtype=dtype)
832
833

        for ind, sp in enumerate(self.domain):
834
835
            casted_x = sp.post_cast(casted_x,
                                    axes=self.domain_axes[ind])
836

837
        return casted_x
csongor's avatar
csongor committed
838

Theo Steininger's avatar
Theo Steininger committed
839
    def _actual_cast(self, x, dtype=None):
840
        if isinstance(x, Field):
csongor's avatar
csongor committed
841
842
843
844
845
            x = x.get_val()

        if dtype is None:
            dtype = self.dtype

846
        return_x = distributed_data_object(
847
848
849
                            global_shape=self.shape,
                            dtype=dtype,
                            distribution_strategy=self.distribution_strategy)
850
851
        return_x.set_full_data(x, copy=False)
        return return_x
Theo Steininger's avatar
Theo Steininger committed
852

853
    def copy(self, domain=None, dtype=None, distribution_strategy=None):
854
        """ Returns a full copy of the Field.
Theo Steininger's avatar
Theo Steininger committed
855

856
857
858
859
860
861
862
863
864
        If no keyword arguments are given, the returned object will be an
        identical copy of the original Field. By explicit specification one is
        able to define the domain, the dtype and the distribution_strategy of
        the returned Field.

        Parameters
        ----------
        domain : DomainObject
            The new domain the Field shall have.
Theo Steininger's avatar
Theo Steininger committed
865

866
867
        dtype : type
            The new dtype the Field shall have.
Theo Steininger's avatar
Theo Steininger committed
868

869
        distribution_strategy : all supported distribution strategies
Theo Steininger's avatar
Theo Steininger committed
870
871
            The new distribution strategy the Field shall have.

872
873
874
875
876
877
878
879
880
881
        Returns
        -------
        out : Field
            The output object. An identical copy of 'self'.

        See Also
        --------
        copy_empty

        """
Theo Steininger's avatar
Theo Steininger committed
882

Theo Steininger's avatar
Theo Steininger committed
883
        copied_val = self.get_val(copy=True)
884
885
886
887
        new_field = self.copy_empty(
                                domain=domain,
                                dtype=dtype,
                                distribution_strategy=distribution_strategy)
Theo Steininger's avatar
Theo Steininger committed
888
889
        new_field.set_val(new_val=copied_val, copy=False)
        return new_field
csongor's avatar
csongor committed
890

891
    def copy_empty(self, domain=None, dtype=None, distribution_strategy=None):
892
893
894
        """ Returns an empty copy of the Field.

        If no keyword arguments are given, the returned object will be an
Theo Steininger's avatar
Theo Steininger committed
895
896
897
898
899
        identical copy of the original Field. The memory for the data array
        is only allocated but not actively set to any value
        (c.f. numpy.ndarray.copy_empty). By explicit specification one is able
        to change the domain, the dtype and the distribution_strategy of the
        returned Field.
Theo Steininger's avatar
Theo Steininger committed
900

901
902
903
904
        Parameters
        ----------
        domain : DomainObject
            The new domain the Field shall have.
Theo Steininger's avatar
Theo Steininger committed
905

906
907
        dtype : type
            The new dtype the Field shall have.
Theo Steininger's avatar
Theo Steininger committed
908

Theo Steininger's avatar
Theo Steininger committed
909
        distribution_strategy : string, all supported distribution strategies
910
            The distribution strategy the new Field should have.
Theo Steininger's avatar
Theo Steininger committed
911

912
913
914
        Returns
        -------
        out : Field
Theo Steininger's avatar
Theo Steininger committed
915
            The output object.
916
917
918
919
920
921

        See Also
        --------
        copy

        """
Theo Steininger's avatar
Theo Steininger committed
922

Theo Steininger's avatar
Theo Steininger committed
923
924
        if domain is None:
            domain = self.domain
csongor's avatar
csongor committed
925
        else:
Theo Steininger's avatar
Theo Steininger committed
926
            domain = self._parse_domain(domain)
csongor's avatar
csongor committed
927

Theo Steininger's avatar
Theo Steininger committed
928
929
930
931
        if dtype is None:
            dtype = self.dtype
        else:
            dtype = np.dtype(dtype)
csongor's avatar
csongor committed
932

933
934
        if distribution_strategy is None:
            distribution_strategy = self.distribution_strategy
csongor's avatar
csongor committed
935

Theo Steininger's avatar
Theo Steininger committed
936
937
938
939
940
941
942
943
944
945
        fast_copyable = True
        try:
            for i in xrange(len(self.domain)):
                if self.domain[i] is not domain[i]:
                    fast_copyable = False
                    break
        except IndexError:
            fast_copyable = False

        if (fast_copyable and dtype == self.dtype and
946
                distribution_strategy == self.distribution_strategy):
Theo Steininger's avatar
Theo Steininger committed
947
948
949
950
            new_field = self._fast_copy_empty()
        else:
            new_field = Field(domain=domain,
                              dtype=dtype,
951
                              distribution_strategy=distribution_strategy)
Theo Steininger's avatar
Theo Steininger committed
952
        return new_field
csongor's avatar
csongor committed
953

Theo Steininger's avatar
Theo Steininger committed
954
955
956
957
958
959
960
    def _fast_copy_empty(self):
        # make an empty field
        new_field = EmptyField()
        # repair its class
        new_field.__class__ = self.__class__
        # copy domain, codomain and val
        for key, value in self.__dict__.items():
961
            if key != '_val':
Theo Steininger's avatar
Theo Steininger committed
962
963
964
965
966
967
                new_field.__dict__[key] = value
            else:
                new_field.__dict__[key] = self.val.copy_empty()
        return new_field

    def weight(self, power=1, inplace=False, spaces=None):
Theo Steininger's avatar
Theo Steininger committed
968
        """ Weights the pixels of `self` with their invidual pixel-volume.
969
970
971
972

        Parameters
        ----------
        power : number
Theo Steininger's avatar
Theo Steininger committed
973
            The pixels get weighted with the volume-factor**power.
Theo Steininger's avatar
Theo Steininger committed
974

975
        inplace : boolean
Theo Steininger's avatar
Theo Steininger committed
976
977
            If True, `self` will be weighted and returned. Otherwise, a copy
            is made.
Theo Steininger's avatar
Theo Steininger committed
978

Theo Steininger's avatar
Theo Steininger committed
979
980
        spaces : tuple of ints
            Determines on which subspace the operation takes place.
Theo Steininger's avatar
Theo Steininger committed
981

982
983
984
        Returns
        -------
        out : Field
Theo Steininger's avatar
Theo Steininger committed
985
            The weighted field.
986
987

        """
988
        if inplace:
csongor's avatar
csongor committed
989
990
991
992
            new_field = self
        else:
            new_field = self.copy_empty()

993
        new_val = self.get_val(copy=False)
csongor's avatar
csongor committed
994

995
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
csongor's avatar
csongor committed
996
        if spaces is None:
Theo Steininger's avatar
Theo Steininger committed
997
            spaces = range(len(self.domain))
csongor's avatar
csongor committed
998

999
        for ind, sp in enumerate(self.domain):
Theo Steininger's avatar
Theo Steininger committed
1000
1001
1002
1003
1004
            if ind in spaces:
                new_val = sp.weight(new_val,
                                    power=power,
                                    axes=self.domain_axes[ind],
                                    inplace=inplace)
1005
1006

        new_field.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
1007
1008
        return new_field

1009
    def dot(self, x=None, spaces=None, bare=False):
Theo Steininger's avatar
Theo Steininger committed
1010
        """ Computes the volume-factor-aware dot product of 'self' with x.
Theo Steininger's avatar
Theo Steininger committed
1011

1012
1013
1014
        Parameters
        ----------
        x : Field
Theo Steininger's avatar
Theo Steininger committed
1015
            The domain of x must contain `self.domain`
Theo Steininger's avatar
Theo Steininger committed
1016

Theo Steininger's avatar
Theo Steininger committed
1017
1018
1019
        spaces : tuple of ints
            If the domain of `self` and `x` are not the same, `spaces` specfies
            the mapping.
Theo Steininger's avatar
Theo Steininger committed
1020

1021
        bare : boolean
Theo Steininger's avatar
Theo Steininger committed
1022
            If true, no volume factors will be included in the computation.
Theo Steininger's avatar
Theo Steininger committed
1023

1024
1025
1026
        Returns
        -------
        out : float, complex
Theo Steininger's avatar
Theo Steininger committed
1027

1028
        """
1029
1030
1031
        if not isinstance(x, Field):
            raise ValueError("The dot-partner must be an instance of " +
                             "the NIFTy field class")
Theo Steininger's avatar
Theo Steininger committed
1032

Martin Reinecke's avatar
Martin Reinecke committed
1033
        # Compute the dot respecting the fact of discrete/continuous spaces
Theo Steininger's avatar
Theo Steininger committed
1034
1035
1036
1037
1038
        if bare:
            y = self
        else:
            y = self.weight(power=1)

1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
        if spaces is None:
            x_val = x.get_val(copy=False)
            y_val = y.get_val(copy=False)
            result = (x_val.conjugate() * y_val).sum()
            return result
        else:
            # create a diagonal operator which is capable of taking care of the
            # axes-matching
            from nifty.operators.diagonal_operator import DiagonalOperator
            diagonal = y.val.conjugate()
            diagonalOperator = DiagonalOperator(domain=y.domain,
                                                diagonal=diagonal,
                                                copy=False)
            dotted = diagonalOperator(x, spaces=spaces)
            return dotted.sum(spaces=spaces)
Theo Steininger's avatar
Theo Steininger committed
1054

1055
    def norm(self, q=2):
1056
        """ Computes the Lq-norm of the field values.
csongor's avatar
csongor committed
1057

Theo Steininger's avatar
Theo Steininger committed
1058
1059
1060
1061
        Parameters
        ----------
        q : scalar
            Parameter q of the Lq-norm (default: 2).
csongor's avatar
csongor committed
1062

Theo Steininger's avatar
Theo Steininger committed
1063
1064
1065
1066
        Returns
        -------
        norm : scalar
            The Lq-norm of the field values.
csongor's avatar
csongor committed
1067
1068

        """
Theo Steininger's avatar
Theo Steininger committed
1069

1070
        if q == 2:
1071
            return (self.dot(x=self)) ** (1 / 2)
csongor's avatar
csongor committed
1072
        else:
1073
            return self.dot(x=self ** (q - 1)) ** (1 / q)
csongor's avatar
csongor committed
1074
1075

    def conjugate(self, inplace=False):
1076
        """ Retruns the complex conjugate of the field.
Theo Steininger's avatar
Theo Steininger committed
1077

1078
1079
1080
        Parameters
        ----------
        inplace : boolean
Theo Steininger's avatar
Theo Steininger committed
1081
            Decides whether the conjugation should be performed inplace.
Theo Steininger's avatar
Theo Steininger committed
1082

1083
1084
1085
1086
        Returns
        -------
        cc : field
            The complex conjugated field.
csongor's avatar
csongor committed
1087
1088

        """
Theo Steininger's avatar
Theo Steininger committed
1089

csongor's avatar
csongor committed
1090
1091