field.py 30.3 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
20
21
from __future__ import division
import numpy as np

Theo Steininger's avatar
Theo Steininger committed
22
23
from keepers import Versionable,\
                    Loggable
Jait Dixit's avatar
Jait Dixit committed
24

25
from d2o import distributed_data_object,\
26
    STRATEGIES as DISTRIBUTION_STRATEGIES
csongor's avatar
csongor committed
27

28
from nifty.config import nifty_configuration as gc
csongor's avatar
csongor committed
29

30
from nifty.domain_object import DomainObject
31

32
from nifty.spaces.power_space import PowerSpace
csongor's avatar
csongor committed
33

csongor's avatar
csongor committed
34
import nifty.nifty_utilities as utilities
35
36
from nifty.random import Random

csongor's avatar
csongor committed
37

Jait Dixit's avatar
Jait Dixit committed
38
class Field(Loggable, Versionable, object):
Theo Steininger's avatar
Theo Steininger committed
39
    # ---Initialization methods---
40

41
    def __init__(self, domain=None, val=None, dtype=None,
42
                 distribution_strategy=None, copy=False):
csongor's avatar
csongor committed
43

44
        self.domain = self._parse_domain(domain=domain, val=val)
45
        self.domain_axes = self._get_axes_tuple(self.domain)
csongor's avatar
csongor committed
46

Theo Steininger's avatar
Theo Steininger committed
47
        self.dtype = self._infer_dtype(dtype=dtype,
Jait Dixit's avatar
Jait Dixit committed
48
                                       val=val,
49
                                       domain=self.domain)
50

51
52
53
        self.distribution_strategy = self._parse_distribution_strategy(
                                distribution_strategy=distribution_strategy,
                                val=val)
csongor's avatar
csongor committed
54

55
56
57
58
        if val is None:
            self._val = None
        else:
            self.set_val(new_val=val, copy=copy)
csongor's avatar
csongor committed
59

60
    def _parse_domain(self, domain, val=None):
61
        if domain is None:
62
63
64
65
            if isinstance(val, Field):
                domain = val.domain
            else:
                domain = ()
66
        elif isinstance(domain, DomainObject):
67
            domain = (domain,)
68
69
70
        elif not isinstance(domain, tuple):
            domain = tuple(domain)

csongor's avatar
csongor committed
71
        for d in domain:
72
            if not isinstance(d, DomainObject):
73
74
                raise TypeError(
                    "Given domain contains something that is not a "
75
                    "DomainObject instance.")
csongor's avatar
csongor committed
76
77
        return domain

Theo Steininger's avatar
Theo Steininger committed
78
79
80
81
82
83
84
85
86
87
    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)
88

89
    def _infer_dtype(self, dtype, val, domain):
csongor's avatar
csongor committed
90
        if dtype is None:
91
92
93
            if isinstance(val, Field) or \
               isinstance(val, distributed_data_object):
                dtype = val.dtype
Theo Steininger's avatar
Theo Steininger committed
94
95
96
            dtype_tuple = (np.dtype(gc['default_field_dtype']),)
        else:
            dtype_tuple = (np.dtype(dtype),)
csongor's avatar
csongor committed
97

Theo Steininger's avatar
Theo Steininger committed
98
        dtype = reduce(lambda x, y: np.result_type(x, y), dtype_tuple)
99

Theo Steininger's avatar
Theo Steininger committed
100
        return dtype
101

102
103
    def _parse_distribution_strategy(self, distribution_strategy, val):
        if distribution_strategy is None:
104
            if isinstance(val, distributed_data_object):
105
                distribution_strategy = val.distribution_strategy
106
            elif isinstance(val, Field):
107
                distribution_strategy = val.distribution_strategy
108
            else:
109
                self.logger.debug("distribution_strategy set to default!")
110
                distribution_strategy = gc['default_distribution_strategy']
111
        elif distribution_strategy not in DISTRIBUTION_STRATEGIES['global']:
112
113
114
            raise ValueError(
                    "distribution_strategy must be a global-type "
                    "strategy.")
115
        return distribution_strategy
116
117

    # ---Factory methods---
118

119
    @classmethod
120
    def from_random(cls, random_type, domain=None, dtype=None,
121
                    distribution_strategy=None, **kwargs):
122
        # create a initially empty field
123
        f = cls(domain=domain, dtype=dtype,
124
                distribution_strategy=distribution_strategy)
125
126
127
128
129
130
131

        # 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
132
        # extract the distributed_data_object from f and apply the appropriate
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
        # 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
160
        else:
161
162
            raise KeyError(
                "unsupported random key '" + str(random_type) + "'.")
csongor's avatar
csongor committed
163

164
        return random_arguments
csongor's avatar
csongor committed
165

166
167
168
169
    # ---Powerspectral methods---

    def power_analyze(self, spaces=None, log=False, nbin=None, binbounds=None,
                      real_signal=True):
Theo Steininger's avatar
Theo Steininger committed
170
        # check if all spaces in `self.domain` are either harmonic or
171
172
173
        # power_space instances
        for sp in self.domain:
            if not sp.harmonic and not isinstance(sp, PowerSpace):
Theo Steininger's avatar
Theo Steininger committed
174
                self.logger.info(
175
                    "Field has a space in `domain` which is neither "
176
177
178
                    "harmonic nor a PowerSpace.")

        # check if the `spaces` input is valid
179
180
181
182
183
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
        if spaces is None:
            if len(self.domain) == 1:
                spaces = (0,)
            else:
184
185
186
                raise ValueError(
                    "Field has multiple spaces as domain "
                    "but `spaces` is None.")
187
188

        if len(spaces) == 0:
189
190
            raise ValueError(
                "No space for analysis specified.")
191
        elif len(spaces) > 1:
192
193
            raise ValueError(
                "Conversion of only one space at a time is allowed.")
194
195
196
197

        space_index = spaces[0]

        if not self.domain[space_index].harmonic:
198
199
            raise ValueError(
                "The analyzed space must be harmonic.")
200

201
202
203
204
205
206
        # 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.

207
208
209
210
        distribution_strategy = \
            self.val.get_axes_local_distribution_strategy(
                self.domain_axes[space_index])

211
212
213
214
215
        if real_signal:
            power_dtype = np.dtype('complex')
        else:
            power_dtype = np.dtype('float')

216
217
        harmonic_domain = self.domain[space_index]
        power_domain = PowerSpace(harmonic_domain=harmonic_domain,
218
                                  distribution_strategy=distribution_strategy,
219
220
                                  log=log, nbin=nbin, binbounds=binbounds,
                                  dtype=power_dtype)
221

222
        # extract pindex and rho from power_domain
223
224
        pindex = power_domain.pindex
        rho = power_domain.rho
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242

        if real_signal:
            hermitian_part, anti_hermitian_part = \
                harmonic_domain.hermitian_decomposition(
                                            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(
243
244
245
246
247
248
249
250
251
                                            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

252
253
254
        result_field = self.copy_empty(
                   domain=result_domain,
                   distribution_strategy=power_spectrum.distribution_strategy)
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
        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']:
283
            raise ValueError("pindex's distribution strategy must be "
284
285
286
287
288
289
                             "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(
290
                    "A slicing distributor shall not be reshaped to "
291
292
293
294
295
296
297
298
299
300
301
302
303
                    "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

304
305
    def power_synthesize(self, spaces=None, real_signal=True,
                         mean=None, std=None):
306

Theo Steininger's avatar
Theo Steininger committed
307
        # check if all spaces in `self.domain` are either of signal-type or
308
309
        # power_space instances
        for sp in self.domain:
310
            if not sp.harmonic and not isinstance(sp, PowerSpace):
Theo Steininger's avatar
Theo Steininger committed
311
                self.logger.info(
312
                    "Field has a space in `domain` which is neither "
313
314
                    "harmonic nor a PowerSpace.")

315
316
317
318
319
320
        # check if the `spaces` input is valid
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
        if spaces is None:
            if len(self.domain) == 1:
                spaces = (0,)
            else:
321
322
323
                raise ValueError(
                    "Field has multiple spaces as domain "
                    "but `spaces` is None.")
324
325

        if len(spaces) == 0:
326
327
            raise ValueError(
                "No space for synthesis specified.")
328
        elif len(spaces) > 1:
329
330
            raise ValueError(
                "Conversion of only one space at a time is allowed.")
331
332
333
334

        power_space_index = spaces[0]
        power_domain = self.domain[power_space_index]
        if not isinstance(power_domain, PowerSpace):
335
336
            raise ValueError(
                "A PowerSpace is needed for field synthetization.")
337
338
339
340
341
342
343
344
345

        # create the result domain
        result_domain = list(self.domain)
        harmonic_domain = power_domain.harmonic_domain
        result_domain[power_space_index] = harmonic_domain

        # create random samples: one or two, depending on whether the
        # power spectrum is real or complex

Martin Reinecke's avatar
Martin Reinecke committed
346
        if issubclass(self.dtype.type, np.complexfloating):
347
348
349
350
            result_list = [None, None]
        else:
            result_list = [None]

351
352
        result_list = [self.__class__.from_random(
                             'normal',
353
354
355
                             mean=mean,
                             std=std,
                             domain=result_domain,
Martin Reinecke's avatar
Martin Reinecke committed
356
                             dtype=self.dtype,
357
                             distribution_strategy=self.distribution_strategy)
358
359
360
361
362
363
364
365
366
                       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
        if real_signal:
            result_val_list = [harmonic_domain.hermitian_decomposition(
                                    x.val,
367
368
                                    axes=x.domain_axes[power_space_index],
                                    preserve_gaussian_variance=True)[0]
369
370
371
372
373
374
375
376
377
378
379
380
381
382
                               for x in result_list]
        else:
            result_val_list = [x.val for x in result_list]

        # weight the random fields with the power spectrum
        # therefore get the pindex from the power space
        pindex = power_domain.pindex
        # 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:
383
            self.logger.warn(
384
                "The distribution_stragey of pindex does not fit the "
385
386
387
388
389
390
                "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)
391
        full_spec = self.val.get_full_data()
392
393
394
395
396

        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
397
        local_rescaler = full_spec[local_blow_up]
398
399
400
401
402
403

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

Martin Reinecke's avatar
Martin Reinecke committed
404
        if issubclass(self.dtype.type, np.complexfloating):
405
406
407
408
409
410
411
412
            result_val_list[1].apply_scalar_function(
                                            lambda x: x * local_rescaler.imag,
                                            inplace=True)

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

Martin Reinecke's avatar
Martin Reinecke committed
413
        if issubclass(self.dtype.type, np.complexfloating):
414
415
416
417
418
            result = result_list[0] + 1j*result_list[1]
        else:
            result = result_list[0]

        return result
419

Theo Steininger's avatar
Theo Steininger committed
420
    # ---Properties---
421

Theo Steininger's avatar
Theo Steininger committed
422
    def set_val(self, new_val=None, copy=False):
423
424
        new_val = self.cast(new_val)
        if copy:
Theo Steininger's avatar
Theo Steininger committed
425
426
            new_val = new_val.copy()
        self._val = new_val
427
        return self
csongor's avatar
csongor committed
428

429
    def get_val(self, copy=False):
430
431
432
        if self._val is None:
            self.set_val(None)

433
        if copy:
Theo Steininger's avatar
Theo Steininger committed
434
            return self._val.copy()
435
        else:
Theo Steininger's avatar
Theo Steininger committed
436
            return self._val
csongor's avatar
csongor committed
437

Theo Steininger's avatar
Theo Steininger committed
438
439
    @property
    def val(self):
440
        return self.get_val(copy=False)
csongor's avatar
csongor committed
441

Theo Steininger's avatar
Theo Steininger committed
442
443
    @val.setter
    def val(self, new_val):
444
        self.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
445

446
447
    @property
    def shape(self):
448
        shape_tuple = tuple(sp.shape for sp in self.domain)
449
450
451
452
        try:
            global_shape = reduce(lambda x, y: x + y, shape_tuple)
        except TypeError:
            global_shape = ()
csongor's avatar
csongor committed
453

454
        return global_shape
csongor's avatar
csongor committed
455

456
457
    @property
    def dim(self):
458
        dim_tuple = tuple(sp.dim for sp in self.domain)
Theo Steininger's avatar
Theo Steininger committed
459
460
461
462
        try:
            return reduce(lambda x, y: x * y, dim_tuple)
        except TypeError:
            return 0
csongor's avatar
csongor committed
463

464
465
    @property
    def dof(self):
Theo Steininger's avatar
Theo Steininger committed
466
467
468
469
470
471
472
473
        dof = self.dim
        if issubclass(self.dtype.type, np.complexfloating):
            dof *= 2
        return dof

    @property
    def total_volume(self):
        volume_tuple = tuple(sp.total_volume for sp in self.domain)
474
        try:
Theo Steininger's avatar
Theo Steininger committed
475
            return reduce(lambda x, y: x * y, volume_tuple)
476
        except TypeError:
Theo Steininger's avatar
Theo Steininger committed
477
            return 0.
478

Theo Steininger's avatar
Theo Steininger committed
479
    # ---Special unary/binary operations---
480

csongor's avatar
csongor committed
481
482
483
    def cast(self, x=None, dtype=None):
        if dtype is None:
            dtype = self.dtype
484
485
        else:
            dtype = np.dtype(dtype)
486

487
488
        casted_x = x

489
        for ind, sp in enumerate(self.domain):
490
            casted_x = sp.pre_cast(casted_x,
491
492
493
                                   axes=self.domain_axes[ind])

        casted_x = self._actual_cast(casted_x, dtype=dtype)
494
495

        for ind, sp in enumerate(self.domain):
496
497
            casted_x = sp.post_cast(casted_x,
                                    axes=self.domain_axes[ind])
498

499
        return casted_x
csongor's avatar
csongor committed
500

Theo Steininger's avatar
Theo Steininger committed
501
    def _actual_cast(self, x, dtype=None):
502
        if isinstance(x, Field):
csongor's avatar
csongor committed
503
504
505
506
507
            x = x.get_val()

        if dtype is None:
            dtype = self.dtype

508
        return_x = distributed_data_object(
509
510
511
                            global_shape=self.shape,
                            dtype=dtype,
                            distribution_strategy=self.distribution_strategy)
512
513
        return_x.set_full_data(x, copy=False)
        return return_x
Theo Steininger's avatar
Theo Steininger committed
514

515
    def copy(self, domain=None, dtype=None, distribution_strategy=None):
Theo Steininger's avatar
Theo Steininger committed
516
        copied_val = self.get_val(copy=True)
517
518
519
520
        new_field = self.copy_empty(
                                domain=domain,
                                dtype=dtype,
                                distribution_strategy=distribution_strategy)
Theo Steininger's avatar
Theo Steininger committed
521
522
        new_field.set_val(new_val=copied_val, copy=False)
        return new_field
csongor's avatar
csongor committed
523

524
    def copy_empty(self, domain=None, dtype=None, distribution_strategy=None):
Theo Steininger's avatar
Theo Steininger committed
525
526
        if domain is None:
            domain = self.domain
csongor's avatar
csongor committed
527
        else:
Theo Steininger's avatar
Theo Steininger committed
528
            domain = self._parse_domain(domain)
csongor's avatar
csongor committed
529

Theo Steininger's avatar
Theo Steininger committed
530
531
532
533
        if dtype is None:
            dtype = self.dtype
        else:
            dtype = np.dtype(dtype)
csongor's avatar
csongor committed
534

535
536
        if distribution_strategy is None:
            distribution_strategy = self.distribution_strategy
csongor's avatar
csongor committed
537

Theo Steininger's avatar
Theo Steininger committed
538
539
540
541
542
543
544
545
546
547
        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
548
                distribution_strategy == self.distribution_strategy):
Theo Steininger's avatar
Theo Steininger committed
549
550
551
552
            new_field = self._fast_copy_empty()
        else:
            new_field = Field(domain=domain,
                              dtype=dtype,
553
                              distribution_strategy=distribution_strategy)
Theo Steininger's avatar
Theo Steininger committed
554
        return new_field
csongor's avatar
csongor committed
555

Theo Steininger's avatar
Theo Steininger committed
556
557
558
559
560
561
562
    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():
563
            if key != '_val':
Theo Steininger's avatar
Theo Steininger committed
564
565
566
567
568
569
                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):
570
        if inplace:
csongor's avatar
csongor committed
571
572
573
574
            new_field = self
        else:
            new_field = self.copy_empty()

575
        new_val = self.get_val(copy=False)
csongor's avatar
csongor committed
576

577
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
csongor's avatar
csongor committed
578
        if spaces is None:
Theo Steininger's avatar
Theo Steininger committed
579
            spaces = range(len(self.domain))
csongor's avatar
csongor committed
580

581
        for ind, sp in enumerate(self.domain):
Theo Steininger's avatar
Theo Steininger committed
582
583
584
585
586
            if ind in spaces:
                new_val = sp.weight(new_val,
                                    power=power,
                                    axes=self.domain_axes[ind],
                                    inplace=inplace)
587
588

        new_field.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
589
590
        return new_field

591
592
593
594
595
    def dot(self, x=None, spaces=None, bare=False):

        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
596

Martin Reinecke's avatar
Martin Reinecke committed
597
        # Compute the dot respecting the fact of discrete/continuous spaces
Theo Steininger's avatar
Theo Steininger committed
598
599
600
601
602
        if bare:
            y = self
        else:
            y = self.weight(power=1)

603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
        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
618

619
    def norm(self, q=2):
csongor's avatar
csongor committed
620
621
622
623
624
625
626
627
628
629
630
631
632
633
        """
            Computes the Lq-norm of the field values.

            Parameters
            ----------
            q : scalar
                Parameter q of the Lq-norm (default: 2).

            Returns
            -------
            norm : scalar
                The Lq-norm of the field values.

        """
634
        if q == 2:
635
            return (self.dot(x=self)) ** (1 / 2)
csongor's avatar
csongor committed
636
        else:
637
            return self.dot(x=self ** (q - 1)) ** (1 / q)
csongor's avatar
csongor committed
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653

    def conjugate(self, inplace=False):
        """
            Computes the complex conjugate of the field.

            Returns
            -------
            cc : field
                The complex conjugated field.

        """
        if inplace:
            work_field = self
        else:
            work_field = self.copy_empty()

654
        new_val = self.get_val(copy=False)
Theo Steininger's avatar
Theo Steininger committed
655
        new_val = new_val.conjugate()
656
        work_field.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
657
658
659

        return work_field

Theo Steininger's avatar
Theo Steininger committed
660
    # ---General unary/contraction methods---
661

Theo Steininger's avatar
Theo Steininger committed
662
663
    def __pos__(self):
        return self.copy()
664

Theo Steininger's avatar
Theo Steininger committed
665
666
667
668
    def __neg__(self):
        return_field = self.copy_empty()
        new_val = -self.get_val(copy=False)
        return_field.set_val(new_val, copy=False)
csongor's avatar
csongor committed
669
670
        return return_field

Theo Steininger's avatar
Theo Steininger committed
671
672
673
674
675
    def __abs__(self):
        return_field = self.copy_empty()
        new_val = abs(self.get_val(copy=False))
        return_field.set_val(new_val, copy=False)
        return return_field
csongor's avatar
csongor committed
676

677
    def _contraction_helper(self, op, spaces):
Theo Steininger's avatar
Theo Steininger committed
678
679
680
681
682
        # build a list of all axes
        if spaces is None:
            spaces = xrange(len(self.domain))
        else:
            spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
csongor's avatar
csongor committed
683

684
        axes_list = tuple(self.domain_axes[sp_index] for sp_index in spaces)
685
686

        try:
Theo Steininger's avatar
Theo Steininger committed
687
            axes_list = reduce(lambda x, y: x+y, axes_list)
688
        except TypeError:
Theo Steininger's avatar
Theo Steininger committed
689
            axes_list = ()
csongor's avatar
csongor committed
690

Theo Steininger's avatar
Theo Steininger committed
691
692
693
        # perform the contraction on the d2o
        data = self.get_val(copy=False)
        data = getattr(data, op)(axis=axes_list)
csongor's avatar
csongor committed
694

Theo Steininger's avatar
Theo Steininger committed
695
696
697
        # check if the result is scalar or if a result_field must be constr.
        if np.isscalar(data):
            return data
csongor's avatar
csongor committed
698
        else:
Theo Steininger's avatar
Theo Steininger committed
699
700
701
            return_domain = tuple(self.domain[i]
                                  for i in xrange(len(self.domain))
                                  if i not in spaces)
702

Theo Steininger's avatar
Theo Steininger committed
703
704
705
706
            return_field = Field(domain=return_domain,
                                 val=data,
                                 copy=False)
            return return_field
csongor's avatar
csongor committed
707

708
709
    def sum(self, spaces=None):
        return self._contraction_helper('sum', spaces)
csongor's avatar
csongor committed
710

711
712
    def prod(self, spaces=None):
        return self._contraction_helper('prod', spaces)
csongor's avatar
csongor committed
713

714
715
    def all(self, spaces=None):
        return self._contraction_helper('all', spaces)
csongor's avatar
csongor committed
716

717
718
    def any(self, spaces=None):
        return self._contraction_helper('any', spaces)
csongor's avatar
csongor committed
719

720
721
    def min(self, spaces=None):
        return self._contraction_helper('min', spaces)
csongor's avatar
csongor committed
722

723
724
    def nanmin(self, spaces=None):
        return self._contraction_helper('nanmin', spaces)
csongor's avatar
csongor committed
725

726
727
    def max(self, spaces=None):
        return self._contraction_helper('max', spaces)
csongor's avatar
csongor committed
728

729
730
    def nanmax(self, spaces=None):
        return self._contraction_helper('nanmax', spaces)
csongor's avatar
csongor committed
731

732
733
    def mean(self, spaces=None):
        return self._contraction_helper('mean', spaces)
csongor's avatar
csongor committed
734

735
736
    def var(self, spaces=None):
        return self._contraction_helper('var', spaces)
csongor's avatar
csongor committed
737

738
739
    def std(self, spaces=None):
        return self._contraction_helper('std', spaces)
csongor's avatar
csongor committed
740

Theo Steininger's avatar
Theo Steininger committed
741
    # ---General binary methods---
csongor's avatar
csongor committed
742

Theo Steininger's avatar
Theo Steininger committed
743
    def _binary_helper(self, other, op, inplace=False):
csongor's avatar
csongor committed
744
        # if other is a field, make sure that the domains match
745
        if isinstance(other, Field):
Theo Steininger's avatar
Theo Steininger committed
746
747
748
749
750
            try:
                assert len(other.domain) == len(self.domain)
                for index in xrange(len(self.domain)):
                    assert other.domain[index] == self.domain[index]
            except AssertionError:
751
752
                raise ValueError(
                    "domains are incompatible.")
Theo Steininger's avatar
Theo Steininger committed
753
            other = other.get_val(copy=False)
csongor's avatar
csongor committed
754

Theo Steininger's avatar
Theo Steininger committed
755
756
        self_val = self.get_val(copy=False)
        return_val = getattr(self_val, op)(other)
csongor's avatar
csongor committed
757
758
759
760

        if inplace:
            working_field = self
        else:
761
            working_field = self.copy_empty(dtype=return_val.dtype)
csongor's avatar
csongor committed
762

Theo Steininger's avatar
Theo Steininger committed
763
        working_field.set_val(return_val, copy=False)
csongor's avatar
csongor committed
764
765
766
        return working_field

    def __add__(self, other):
Theo Steininger's avatar
Theo Steininger committed
767
        return self._binary_helper(other, op='__add__')
768

769
    def __radd__(self, other):
Theo Steininger's avatar
Theo Steininger committed
770
        return self._binary_helper(other, op='__radd__')
csongor's avatar
csongor committed
771
772

    def __iadd__(self, other):
Theo Steininger's avatar
Theo Steininger committed
773
        return self._binary_helper(other, op='__iadd__', inplace=True)
csongor's avatar
csongor committed
774
775

    def __sub__(self, other):
Theo Steininger's avatar
Theo Steininger committed
776
        return self._binary_helper(other, op='__sub__')
csongor's avatar
csongor committed
777
778

    def __rsub__(self, other):
Theo Steininger's avatar
Theo Steininger committed
779
        return self._binary_helper(other, op='__rsub__')
csongor's avatar
csongor committed
780
781

    def __isub__(self, other):
Theo Steininger's avatar
Theo Steininger committed
782
        return self._binary_helper(other, op='__isub__', inplace=True)
csongor's avatar
csongor committed
783
784

    def __mul__(self, other):
Theo Steininger's avatar
Theo Steininger committed
785
        return self._binary_helper(other, op='__mul__')
786

787
    def __rmul__(self, other):
Theo Steininger's avatar
Theo Steininger committed
788
        return self._binary_helper(other, op='__rmul__')
csongor's avatar
csongor committed
789
790

    def __imul__(self, other):
Theo Steininger's avatar
Theo Steininger committed
791
        return self._binary_helper(other, op='__imul__', inplace=True)
csongor's avatar
csongor committed
792
793

    def __div__(self, other):
Theo Steininger's avatar
Theo Steininger committed
794
        return self._binary_helper(other, op='__div__')
csongor's avatar
csongor committed
795
796

    def __rdiv__(self, other):
Theo Steininger's avatar
Theo Steininger committed
797
        return self._binary_helper(other, op='__rdiv__')
csongor's avatar
csongor committed
798
799

    def __idiv__(self, other):
Theo Steininger's avatar
Theo Steininger committed
800
        return self._binary_helper(other, op='__idiv__', inplace=True)
801

csongor's avatar
csongor committed
802
    def __pow__(self, other):
Theo Steininger's avatar
Theo Steininger committed
803
        return self._binary_helper(other, op='__pow__')
csongor's avatar
csongor committed
804
805

    def __rpow__(self, other):
Theo Steininger's avatar
Theo Steininger committed
806
        return self._binary_helper(other, op='__rpow__')
csongor's avatar
csongor committed
807
808

    def __ipow__(self, other):
Theo Steininger's avatar
Theo Steininger committed
809
        return self._binary_helper(other, op='__ipow__', inplace=True)
csongor's avatar
csongor committed
810
811

    def __lt__(self, other):
Theo Steininger's avatar
Theo Steininger committed
812
        return self._binary_helper(other, op='__lt__')
csongor's avatar
csongor committed
813
814

    def __le__(self, other):
Theo Steininger's avatar
Theo Steininger committed
815
        return self._binary_helper(other, op='__le__')
csongor's avatar
csongor committed
816
817
818
819
820

    def __ne__(self, other):
        if other is None:
            return True
        else:
Theo Steininger's avatar
Theo Steininger committed
821
            return self._binary_helper(other, op='__ne__')
csongor's avatar
csongor committed
822
823
824
825
826

    def __eq__(self, other):
        if other is None:
            return False
        else:
Theo Steininger's avatar
Theo Steininger committed
827
            return self._binary_helper(other, op='__eq__')
csongor's avatar
csongor committed
828
829

    def __ge__(self, other):
Theo Steininger's avatar
Theo Steininger committed
830
        return self._binary_helper(other, op='__ge__')
csongor's avatar
csongor committed
831
832

    def __gt__(self, other):
Theo Steininger's avatar
Theo Steininger committed
833
834
835
836
837
838
839
840
841
842
843
844
845
        return self._binary_helper(other, op='__gt__')

    def __repr__(self):
        return "<nifty_core.field>"

    def __str__(self):
        minmax = [self.min(), self.max()]
        mean = self.mean()
        return "nifty_core.field instance\n- domain      = " + \
               repr(self.domain) + \
               "\n- val         = " + repr(self.get_val()) + \
               "\n  - min.,max. = " + str(minmax) + \
               "\n  - mean = " + str(mean)
csongor's avatar
csongor committed
846

Jait Dixit's avatar
Jait Dixit committed
847
848
849
    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
Theo Steininger's avatar
Theo Steininger committed
850
851
852
        hdf5_group.attrs['dtype'] = self.dtype.name
        hdf5_group.attrs['distribution_strategy'] = self.distribution_strategy
        hdf5_group.attrs['domain_axes'] = str(self.domain_axes)
853
        hdf5_group['num_domain'] = len(self.domain)
Jait Dixit's avatar
Jait Dixit committed
854

Theo Steininger's avatar
Theo Steininger committed
855
856
857
858
        if self._val is None:
            ret_dict = {}
        else:
            ret_dict = {'val': self.val}
Jait Dixit's avatar
Jait Dixit committed
859
860
861
862
863
864
865

        for i in range(len(self.domain)):
            ret_dict['s_' + str(i)] = self.domain[i]

        return ret_dict

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
866
    def _from_hdf5(cls, hdf5_group, repository):
Jait Dixit's avatar
Jait Dixit committed
867
868
869
870
871
872
        # create empty field
        new_field = EmptyField()
        # reset class
        new_field.__class__ = cls
        # set values
        temp_domain = []
873
        for i in range(hdf5_group['num_domain'][()]):
Theo Steininger's avatar
Theo Steininger committed
874
            temp_domain.append(repository.get('s_' + str(i), hdf5_group))
Jait Dixit's avatar
Jait Dixit committed
875
876
        new_field.domain = tuple(temp_domain)

Theo Steininger's avatar
Theo Steininger committed
877
        exec('new_field.domain_axes = ' + hdf5_group.attrs['domain_axes'])
Theo Steininger's avatar
Theo Steininger committed
878
879
880
881
882
883

        try:
            new_field._val = repository.get('val', hdf5_group)
        except(KeyError):
            new_field._val = None

Theo Steininger's avatar
Theo Steininger committed
884
885
886
        new_field.dtype = np.dtype(hdf5_group.attrs['dtype'])
        new_field.distribution_strategy =\
            hdf5_group.attrs['distribution_strategy']
Jait Dixit's avatar
Jait Dixit committed
887
888

        return new_field
889

Theo Steininger's avatar
Theo Steininger committed
890

891
class EmptyField(Field):
csongor's avatar
csongor committed
892
893
    def __init__(self):
        pass