field.py 31 KB
Newer Older
csongor's avatar
csongor committed
1
2
3
from __future__ import division
import numpy as np

4
from d2o import distributed_data_object,\
5
    STRATEGIES as DISTRIBUTION_STRATEGIES
csongor's avatar
csongor committed
6

7
8
9
from nifty.config import about,\
                         nifty_configuration as gc,\
                         dependency_injector as gdi
csongor's avatar
csongor committed
10

11
from nifty.field_types import FieldType
12

13
from nifty.spaces.space import Space
14
from nifty.spaces.power_space import PowerSpace
csongor's avatar
csongor committed
15

csongor's avatar
csongor committed
16
import nifty.nifty_utilities as utilities
17
18
from nifty.random import Random

csongor's avatar
csongor committed
19
20

POINT_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']
theos's avatar
theos committed
21
COMM = getattr(gdi[gc['mpi_module']], gc['default_comm'])
csongor's avatar
csongor committed
22
23


24
class Field(object):
theos's avatar
theos committed
25
    # ---Initialization methods---
26

theos's avatar
theos committed
27
28
    def __init__(self, domain=None, val=None, dtype=None, field_type=None,
                 datamodel=None, copy=False):
csongor's avatar
csongor committed
29

30
        self.domain = self._parse_domain(domain=domain, val=val)
31
        self.domain_axes = self._get_axes_tuple(self.domain)
csongor's avatar
csongor committed
32

33
        self.field_type = self._parse_field_type(field_type, val=val)
34

theos's avatar
theos committed
35
36
37
38
39
40
        try:
            start = len(reduce(lambda x, y: x+y, self.domain_axes))
        except TypeError:
            start = 0
        self.field_type_axes = self._get_axes_tuple(self.field_type,
                                                    start=start)
41

theos's avatar
theos committed
42
        self.dtype = self._infer_dtype(dtype=dtype,
Jait Dixit's avatar
Jait Dixit committed
43
                                       val=val,
theos's avatar
theos committed
44
45
                                       domain=self.domain,
                                       field_type=self.field_type)
46

theos's avatar
theos committed
47
48
        self.datamodel = self._parse_datamodel(datamodel=datamodel,
                                               val=val)
csongor's avatar
csongor committed
49
50
51

        self.set_val(new_val=val, copy=copy)

52
    def _parse_domain(self, domain, val=None):
53
        if domain is None:
54
55
56
57
            if isinstance(val, Field):
                domain = val.domain
            else:
                domain = ()
58
        elif isinstance(domain, Space):
59
            domain = (domain,)
60
61
62
        elif not isinstance(domain, tuple):
            domain = tuple(domain)

csongor's avatar
csongor committed
63
        for d in domain:
64
            if not isinstance(d, Space):
csongor's avatar
csongor committed
65
                raise TypeError(about._errors.cstring(
66
67
                    "ERROR: Given domain contains something that is not a "
                    "nifty.space."))
csongor's avatar
csongor committed
68
69
        return domain

70
    def _parse_field_type(self, field_type, val=None):
71
        if field_type is None:
72
73
74
75
            if isinstance(val, Field):
                field_type = val.field_type
            else:
                field_type = ()
76
        elif isinstance(field_type, FieldType):
77
            field_type = (field_type,)
78
79
        elif not isinstance(field_type, tuple):
            field_type = tuple(field_type)
80
        for ft in field_type:
81
            if not isinstance(ft, FieldType):
82
                raise TypeError(about._errors.cstring(
83
                    "ERROR: Given object is not a nifty.FieldType."))
84
85
        return field_type

theos's avatar
theos committed
86
87
88
89
90
91
92
93
94
95
    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)
96

97
    def _infer_dtype(self, dtype, val, domain, field_type):
csongor's avatar
csongor committed
98
        if dtype is None:
99
100
101
            if isinstance(val, Field) or \
               isinstance(val, distributed_data_object):
                dtype = val.dtype
theos's avatar
theos committed
102
103
104
105
106
107
108
            dtype_tuple = (np.dtype(gc['default_field_dtype']),)
        else:
            dtype_tuple = (np.dtype(dtype),)
        if domain is not None:
            dtype_tuple += tuple(np.dtype(sp.dtype) for sp in domain)
        if field_type is not None:
            dtype_tuple += tuple(np.dtype(ft.dtype) for ft in field_type)
csongor's avatar
csongor committed
109

theos's avatar
theos committed
110
        dtype = reduce(lambda x, y: np.result_type(x, y), dtype_tuple)
111

theos's avatar
theos committed
112
        return dtype
113

theos's avatar
theos committed
114
    def _parse_datamodel(self, datamodel, val):
115
116
117
118
119
120
121
122
123
124
125
126
127
128
        if datamodel is None:
            if isinstance(val, distributed_data_object):
                datamodel = val.distribution_strategy
            elif isinstance(val, Field):
                datamodel = val.datamodel
            else:
                about.warnings.cprint("WARNING: Datamodel set to default!")
                datamodel = gc['default_datamodel']
        elif datamodel not in DISTRIBUTION_STRATEGIES['all']:
            raise ValueError(about._errors.cstring(
                    "ERROR: Invalid datamodel!"))
        return datamodel

    # ---Factory methods---
129

130
131
132
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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
    @classmethod
    def from_random(cls, random_type, domain=None, dtype=None, field_type=None,
                    datamodel=None, **kwargs):
        # create a initially empty field
        f = cls(domain=domain, dtype=dtype, field_type=field_type,
                datamodel=datamodel)

        # 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)

        # extract the distributed_dato_object from f and apply the appropriate
        # 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}

#        elif random_type == 'syn':
#            pass

csongor's avatar
csongor committed
174
        else:
175
176
            raise KeyError(about._errors.cstring(
                "ERROR: unsupported random key '" + str(random_type) + "'."))
csongor's avatar
csongor committed
177

178
        return random_arguments
csongor's avatar
csongor committed
179

180
181
182
183
184
185
186
187
188
189
190
191
192
    # ---Powerspectral methods---

    def power_analyze(self, spaces=None, log=False, nbin=None, binbounds=None,
                      real_signal=True):
        # assert that all spaces in `self.domain` are either harmonic or
        # power_space instances
        for sp in self.domain:
            if not sp.harmonic and not isinstance(sp, PowerSpace):
                raise AttributeError(
                    "ERROR: Field has a space in `domain` which is neither "
                    "harmonic nor a PowerSpace.")

        # check if the `spaces` input is valid
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
        spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
        if spaces is None:
            if len(self.domain) == 1:
                spaces = (0,)
            else:
                raise ValueError(about._errors.cstring(
                    "ERROR: Field has multiple spaces as domain "
                    "but `spaces` is None."))

        if len(spaces) == 0:
            raise ValueError(about._errors.cstring(
                "ERROR: No space for analysis specified."))
        elif len(spaces) > 1:
            raise ValueError(about._errors.cstring(
                "ERROR: Conversion of only one space at a time is allowed."))

        space_index = spaces[0]

        if not self.domain[space_index].harmonic:
            raise ValueError(about._errors.cstring(
                "ERROR: Conversion of only one space at a time is allowed."))

215
216
217
218
219
220
        # 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.

221
222
223
224
        distribution_strategy = \
            self.val.get_axes_local_distribution_strategy(
                self.domain_axes[space_index])

225
226
227
228
229
        if real_signal:
            power_dtype = np.dtype('complex')
        else:
            power_dtype = np.dtype('float')

230
231
232
        harmonic_domain = self.domain[space_index]
        power_domain = PowerSpace(harmonic_domain=harmonic_domain,
                                  datamodel=distribution_strategy,
233
234
                                  log=log, nbin=nbin, binbounds=binbounds,
                                  dtype=power_dtype)
235

236
        # extract pindex and rho from power_domain
237
238
        pindex = power_domain.pindex
        rho = power_domain.rho
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256

        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(
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
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
                                            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

        result_field = self.copy_empty(domain=result_domain)
        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']:
            raise ValueError("ERROR: pindex's distribution strategy must be "
                             "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(
                    "ERROR: A slicing distributor shall not be reshaped to "
                    "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

316
    def power_synthesize(self, spaces=None, real_signal=True):
317
        # assert that all spaces in `self.domain` are either of signal-type or
318
319
        # power_space instances
        for sp in self.domain:
320
            if not sp.harmonic and not isinstance(sp, PowerSpace):
321
322
323
324
                raise AttributeError(
                    "ERROR: Field has a space in `domain` which is neither "
                    "harmonic nor a PowerSpace.")

325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
        # 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:
                raise ValueError(about._errors.cstring(
                    "ERROR: Field has multiple spaces as domain "
                    "but `spaces` is None."))

        if len(spaces) == 0:
            raise ValueError(about._errors.cstring(
                "ERROR: No space for synthesis specified."))
        elif len(spaces) > 1:
            raise ValueError(about._errors.cstring(
                "ERROR: Conversion of only one space at a time is allowed."))

        power_space_index = spaces[0]
        power_domain = self.domain[power_space_index]
        if not isinstance(power_domain, PowerSpace):
            raise ValueError(about._errors.cstring(
                "ERROR: A PowerSpace is needed for field synthetization."))

        # 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

        if issubclass(power_domain.dtype.type, np.complexfloating):
            result_list = [None, None]
        else:
            result_list = [None]

        result_list = [self.__class__.from_random('normal',
                                                  result_domain,
                                                  dtype=harmonic_domain.dtype,
                                                  field_type=self.field_type,
                                                  datamodel=self.datamodel)
                       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,
                                    axes=x.domain_axes[power_space_index])[0]
                               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:
            about.warnings.cprint(
                "WARNING: The distribution_stragey of pindex does not fit the "
                "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_spec = self.val.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
        local_rescaler = local_spec[local_blow_up]

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

        if issubclass(power_domain.dtype.type, np.complexfloating):
            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)]

        if issubclass(power_domain.dtype.type, np.complexfloating):
            result = result_list[0] + 1j*result_list[1]
        else:
            result = result_list[0]

        return result
426

theos's avatar
theos committed
427
    # ---Properties---
428

theos's avatar
theos committed
429
    def set_val(self, new_val=None, copy=False):
430
431
        new_val = self.cast(new_val)
        if copy:
theos's avatar
theos committed
432
433
434
            new_val = new_val.copy()
        self._val = new_val
        return self._val
csongor's avatar
csongor committed
435

436
437
    def get_val(self, copy=False):
        if copy:
theos's avatar
theos committed
438
            return self._val.copy()
439
        else:
theos's avatar
theos committed
440
            return self._val
csongor's avatar
csongor committed
441

theos's avatar
theos committed
442
443
444
    @property
    def val(self):
        return self._val
csongor's avatar
csongor committed
445

theos's avatar
theos committed
446
447
448
    @val.setter
    def val(self, new_val):
        self._val = self.cast(new_val)
csongor's avatar
csongor committed
449

450
451
    @property
    def shape(self):
452
453
454
455
456
457
458
        shape_tuple = ()
        shape_tuple += tuple(sp.shape for sp in self.domain)
        shape_tuple += tuple(ft.shape for ft in self.field_type)
        try:
            global_shape = reduce(lambda x, y: x + y, shape_tuple)
        except TypeError:
            global_shape = ()
csongor's avatar
csongor committed
459

460
        return global_shape
csongor's avatar
csongor committed
461

462
463
    @property
    def dim(self):
theos's avatar
theos committed
464
465
466
467
468
469
470
        dim_tuple = ()
        dim_tuple += tuple(sp.dim for sp in self.domain)
        dim_tuple += tuple(ft.dim for ft in self.field_type)
        try:
            return reduce(lambda x, y: x * y, dim_tuple)
        except TypeError:
            return 0
csongor's avatar
csongor committed
471

472
473
    @property
    def dof(self):
theos's avatar
theos committed
474
475
476
477
478
479
480
481
        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)
482
        try:
theos's avatar
theos committed
483
            return reduce(lambda x, y: x * y, volume_tuple)
484
        except TypeError:
theos's avatar
theos committed
485
            return 0
486

theos's avatar
theos committed
487
    # ---Special unary/binary operations---
488

csongor's avatar
csongor committed
489
490
491
    def cast(self, x=None, dtype=None):
        if dtype is None:
            dtype = self.dtype
492
493
        else:
            dtype = np.dtype(dtype)
494

theos's avatar
theos committed
495
        casted_x = self._actual_cast(x, dtype=dtype)
496
497

        for ind, sp in enumerate(self.domain):
498
            casted_x = sp.complement_cast(casted_x,
theos's avatar
theos committed
499
                                          axes=self.domain_axes[ind])
500
501
502

        for ind, ft in enumerate(self.field_type):
            casted_x = ft.complement_cast(casted_x,
theos's avatar
theos committed
503
                                          axes=self.field_type_axes[ind])
504
505

        return casted_x
csongor's avatar
csongor committed
506

theos's avatar
theos committed
507
    def _actual_cast(self, x, dtype=None):
508
        if isinstance(x, Field):
csongor's avatar
csongor committed
509
510
511
512
513
            x = x.get_val()

        if dtype is None:
            dtype = self.dtype

514
515
516
517
        return_x = distributed_data_object(
                                        global_shape=self.shape,
                                        dtype=dtype,
                                        distribution_strategy=self.datamodel)
518
519
        return_x.set_full_data(x, copy=False)
        return return_x
theos's avatar
theos committed
520
521
522
523
524
525
526
527
528
529

    def copy(self, domain=None, dtype=None, field_type=None,
             datamodel=None):
        copied_val = self.get_val(copy=True)
        new_field = self.copy_empty(domain=domain,
                                    dtype=dtype,
                                    field_type=field_type,
                                    datamodel=datamodel)
        new_field.set_val(new_val=copied_val, copy=False)
        return new_field
csongor's avatar
csongor committed
530

theos's avatar
theos committed
531
532
533
534
    def copy_empty(self, domain=None, dtype=None, field_type=None,
                   datamodel=None):
        if domain is None:
            domain = self.domain
csongor's avatar
csongor committed
535
        else:
theos's avatar
theos committed
536
            domain = self._parse_domain(domain)
csongor's avatar
csongor committed
537

theos's avatar
theos committed
538
539
540
541
        if dtype is None:
            dtype = self.dtype
        else:
            dtype = np.dtype(dtype)
csongor's avatar
csongor committed
542

theos's avatar
theos committed
543
544
545
546
        if field_type is None:
            field_type = self.field_type
        else:
            field_type = self._parse_field_type(field_type)
csongor's avatar
csongor committed
547

theos's avatar
theos committed
548
549
        if datamodel is None:
            datamodel = self.datamodel
csongor's avatar
csongor committed
550

theos's avatar
theos committed
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
        fast_copyable = True
        try:
            for i in xrange(len(self.domain)):
                if self.domain[i] is not domain[i]:
                    fast_copyable = False
                    break
            for i in xrange(len(self.field_type)):
                if self.field_type[i] is not field_type[i]:
                    fast_copyable = False
                    break
        except IndexError:
            fast_copyable = False

        if (fast_copyable and dtype == self.dtype and
                datamodel == self.datamodel):
            new_field = self._fast_copy_empty()
        else:
            new_field = Field(domain=domain,
                              dtype=dtype,
                              field_type=field_type,
                              datamodel=datamodel)
        return new_field
csongor's avatar
csongor committed
573

theos's avatar
theos committed
574
575
576
577
578
579
580
581
582
583
584
585
586
587
    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():
            if key != 'val':
                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):
588
        if inplace:
csongor's avatar
csongor committed
589
590
591
592
            new_field = self
        else:
            new_field = self.copy_empty()

593
        new_val = self.get_val(copy=False)
csongor's avatar
csongor committed
594

csongor's avatar
csongor committed
595
        if spaces is None:
theos's avatar
theos committed
596
597
598
            spaces = range(len(self.domain))
        else:
            spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
csongor's avatar
csongor committed
599

600
        for ind, sp in enumerate(self.domain):
theos's avatar
theos committed
601
602
603
604
605
            if ind in spaces:
                new_val = sp.weight(new_val,
                                    power=power,
                                    axes=self.domain_axes[ind],
                                    inplace=inplace)
606
607

        new_field.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
608
609
        return new_field

theos's avatar
theos committed
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
    def dot(self, x=None, bare=False):
        if isinstance(x, Field):
            try:
                assert len(x.domain) == len(self.domain)
                for index in xrange(len(self.domain)):
                    assert x.domain[index] == self.domain[index]
                for index in xrange(len(self.field_type)):
                    assert x.field_type[index] == self.field_type[index]
            except AssertionError:
                raise ValueError(about._errors.cstring(
                    "ERROR: domains are incompatible."))
            # extract the data from x and try to dot with this
            x = x.get_val(copy=False)

        # Compute the dot respecting the fact of discrete/continous spaces
        if bare:
            y = self
        else:
            y = self.weight(power=1)

        y = y.get_val(copy=False)

        # Cast the input in order to cure dtype and shape differences
        x = self.cast(x)

        dotted = x.conjugate() * y

        return dotted.sum()

639
    def norm(self, q=2):
csongor's avatar
csongor committed
640
641
642
643
644
645
646
647
648
649
650
651
652
653
        """
            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.

        """
654
        if q == 2:
655
            return (self.dot(x=self)) ** (1 / 2)
csongor's avatar
csongor committed
656
        else:
657
            return self.dot(x=self ** (q - 1)) ** (1 / q)
csongor's avatar
csongor committed
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673

    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()

674
        new_val = self.get_val(copy=False)
theos's avatar
theos committed
675
        new_val = new_val.conjugate()
676
        work_field.set_val(new_val=new_val, copy=False)
csongor's avatar
csongor committed
677
678
679

        return work_field

theos's avatar
theos committed
680
    # ---General unary/contraction methods---
681

theos's avatar
theos committed
682
683
    def __pos__(self):
        return self.copy()
684

theos's avatar
theos committed
685
686
687
688
    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
689
690
        return return_field

theos's avatar
theos committed
691
692
693
694
695
    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
696

theos's avatar
theos committed
697
698
699
700
701
702
    def _contraction_helper(self, op, spaces, types):
        # 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
703

theos's avatar
theos committed
704
705
706
707
        if types is None:
            types = xrange(len(self.field_type))
        else:
            types = utilities.cast_axis_to_tuple(types, len(self.field_type))
708

theos's avatar
theos committed
709
710
711
712
        axes_list = ()
        axes_list += tuple(self.domain_axes[sp_index] for sp_index in spaces)
        axes_list += tuple(self.field_type_axes[ft_index] for
                           ft_index in types)
713
        try:
theos's avatar
theos committed
714
            axes_list = reduce(lambda x, y: x+y, axes_list)
715
        except TypeError:
theos's avatar
theos committed
716
            axes_list = ()
csongor's avatar
csongor committed
717

theos's avatar
theos committed
718
719
720
        # perform the contraction on the d2o
        data = self.get_val(copy=False)
        data = getattr(data, op)(axis=axes_list)
csongor's avatar
csongor committed
721

theos's avatar
theos committed
722
723
724
        # 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
725
        else:
theos's avatar
theos committed
726
727
728
729
730
731
732
733
734
735
736
            return_domain = tuple(self.domain[i]
                                  for i in xrange(len(self.domain))
                                  if i not in spaces)
            return_field_type = tuple(self.field_type[i]
                                      for i in xrange(len(self.field_type))
                                      if i not in types)
            return_field = Field(domain=return_domain,
                                 val=data,
                                 field_type=return_field_type,
                                 copy=False)
            return return_field
csongor's avatar
csongor committed
737

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

theos's avatar
theos committed
741
742
    def prod(self, spaces=None, types=None):
        return self._contraction_helper('prod', spaces, types)
csongor's avatar
csongor committed
743

theos's avatar
theos committed
744
745
    def all(self, spaces=None, types=None):
        return self._contraction_helper('all', spaces, types)
csongor's avatar
csongor committed
746

theos's avatar
theos committed
747
748
    def any(self, spaces=None, types=None):
        return self._contraction_helper('any', spaces, types)
csongor's avatar
csongor committed
749

theos's avatar
theos committed
750
751
    def min(self, spaces=None, types=None):
        return self._contraction_helper('min', spaces, types)
csongor's avatar
csongor committed
752

theos's avatar
theos committed
753
754
    def nanmin(self, spaces=None, types=None):
        return self._contraction_helper('nanmin', spaces, types)
csongor's avatar
csongor committed
755

theos's avatar
theos committed
756
757
    def max(self, spaces=None, types=None):
        return self._contraction_helper('max', spaces, types)
csongor's avatar
csongor committed
758

theos's avatar
theos committed
759
760
    def nanmax(self, spaces=None, types=None):
        return self._contraction_helper('nanmax', spaces, types)
csongor's avatar
csongor committed
761

theos's avatar
theos committed
762
763
    def mean(self, spaces=None, types=None):
        return self._contraction_helper('mean', spaces, types)
csongor's avatar
csongor committed
764

theos's avatar
theos committed
765
766
    def var(self, spaces=None, types=None):
        return self._contraction_helper('var', spaces, types)
csongor's avatar
csongor committed
767

theos's avatar
theos committed
768
769
    def std(self, spaces=None, types=None):
        return self._contraction_helper('std', spaces, types)
csongor's avatar
csongor committed
770

theos's avatar
theos committed
771
    # ---General binary methods---
csongor's avatar
csongor committed
772

theos's avatar
theos committed
773
    def _binary_helper(self, other, op, inplace=False):
csongor's avatar
csongor committed
774
        # if other is a field, make sure that the domains match
775
        if isinstance(other, Field):
theos's avatar
theos committed
776
777
778
779
            try:
                assert len(other.domain) == len(self.domain)
                for index in xrange(len(self.domain)):
                    assert other.domain[index] == self.domain[index]
780
                assert len(other.field_type) == len(self.field_type)
theos's avatar
theos committed
781
782
783
784
785
786
                for index in xrange(len(self.field_type)):
                    assert other.field_type[index] == self.field_type[index]
            except AssertionError:
                raise ValueError(about._errors.cstring(
                    "ERROR: domains are incompatible."))
            other = other.get_val(copy=False)
csongor's avatar
csongor committed
787

theos's avatar
theos committed
788
789
        self_val = self.get_val(copy=False)
        return_val = getattr(self_val, op)(other)
csongor's avatar
csongor committed
790
791
792
793
794
795

        if inplace:
            working_field = self
        else:
            working_field = self.copy_empty()

theos's avatar
theos committed
796
        working_field.set_val(return_val, copy=False)
csongor's avatar
csongor committed
797
798
799
        return working_field

    def __add__(self, other):
theos's avatar
theos committed
800
        return self._binary_helper(other, op='__add__')
801

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

    def __iadd__(self, other):
theos's avatar
theos committed
806
        return self._binary_helper(other, op='__iadd__', inplace=True)
csongor's avatar
csongor committed
807
808

    def __sub__(self, other):
theos's avatar
theos committed
809
        return self._binary_helper(other, op='__sub__')
csongor's avatar
csongor committed
810
811

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

    def __isub__(self, other):
theos's avatar
theos committed
815
        return self._binary_helper(other, op='__isub__', inplace=True)
csongor's avatar
csongor committed
816
817

    def __mul__(self, other):
theos's avatar
theos committed
818
        return self._binary_helper(other, op='__mul__')
819

820
    def __rmul__(self, other):
theos's avatar
theos committed
821
        return self._binary_helper(other, op='__rmul__')
csongor's avatar
csongor committed
822
823

    def __imul__(self, other):
theos's avatar
theos committed
824
        return self._binary_helper(other, op='__imul__', inplace=True)
csongor's avatar
csongor committed
825
826

    def __div__(self, other):
theos's avatar
theos committed
827
        return self._binary_helper(other, op='__div__')
csongor's avatar
csongor committed
828
829

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

    def __idiv__(self, other):
theos's avatar
theos committed
833
        return self._binary_helper(other, op='__idiv__', inplace=True)
834

csongor's avatar
csongor committed
835
    def __pow__(self, other):
theos's avatar
theos committed
836
        return self._binary_helper(other, op='__pow__')
csongor's avatar
csongor committed
837
838

    def __rpow__(self, other):
theos's avatar
theos committed
839
        return self._binary_helper(other, op='__rpow__')
csongor's avatar
csongor committed
840
841

    def __ipow__(self, other):
theos's avatar
theos committed
842
        return self._binary_helper(other, op='__ipow__', inplace=True)
csongor's avatar
csongor committed
843
844

    def __lt__(self, other):
theos's avatar
theos committed
845
        return self._binary_helper(other, op='__lt__')
csongor's avatar
csongor committed
846
847

    def __le__(self, other):
theos's avatar
theos committed
848
        return self._binary_helper(other, op='__le__')
csongor's avatar
csongor committed
849
850
851
852
853

    def __ne__(self, other):
        if other is None:
            return True
        else:
theos's avatar
theos committed
854
            return self._binary_helper(other, op='__ne__')
csongor's avatar
csongor committed
855
856
857
858
859

    def __eq__(self, other):
        if other is None:
            return False
        else:
theos's avatar
theos committed
860
            return self._binary_helper(other, op='__eq__')
csongor's avatar
csongor committed
861
862

    def __ge__(self, other):
theos's avatar
theos committed
863
        return self._binary_helper(other, op='__ge__')
csongor's avatar
csongor committed
864
865

    def __gt__(self, other):
theos's avatar
theos committed
866
867
868
869
870
871
872
873
874
875
876
877
878
        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
879

880

881
class EmptyField(Field):
csongor's avatar
csongor committed
882
883
    def __init__(self):
        pass