field.py 21.4 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# 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/>.
Theo Steininger's avatar
Theo Steininger committed
13
#
Martin Reinecke's avatar
Martin Reinecke committed
14
# Copyright(C) 2013-2018 Max-Planck-Society
Theo Steininger's avatar
Theo Steininger committed
15
16
17
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
18

19
from __future__ import absolute_import, division, print_function
20

csongor's avatar
csongor committed
21
import numpy as np
22
23
24

from . import dobj, utilities
from .compat import *
Martin Reinecke's avatar
Martin Reinecke committed
25
from .domain_tuple import DomainTuple
26

27

Martin Reinecke's avatar
Martin Reinecke committed
28
class Field(object):
Theo Steininger's avatar
Theo Steininger committed
29
30
    """ The discrete representation of a continuous field over multiple spaces.

Martin Reinecke's avatar
Martin Reinecke committed
31
    In NIFTy, Fields are used to store data arrays and carry all the needed
32
    metainformation (i.e. the domain) for operators to be able to work on them.
Theo Steininger's avatar
Theo Steininger committed
33

34
35
    Parameters
    ----------
36
37
    domain : DomainTuple
        the domain of the new Field
Theo Steininger's avatar
Theo Steininger committed
38

39
40
41
    val : data_object
        This object's global shape must match the domain shape
        After construction, the object will no longer be writeable!
Martin Reinecke's avatar
Martin Reinecke committed
42
43
44
45

    Notes
    -----
    If possible, do not invoke the constructor directly, but use one of the
46
    many convenience functions for Field construction!
47
    """
48

49
50
51
52
53
54
55
56
57
    def __init__(self, domain, val):
        if not isinstance(domain, DomainTuple):
            raise TypeError("domain must be of type DomainTuple")
        if not isinstance(val, dobj.data_object):
            raise TypeError("val must be of type dobj.data_object")
        if domain.shape != val.shape:
            raise ValueError("mismatch between the shapes of val and domain")
        self._domain = domain
        self._val = val
58
        dobj.lock(self._val)
Martin Reinecke's avatar
Martin Reinecke committed
59

60
61
62
63
64
65
66
    # prevent implicit conversion to bool
    def __nonzero__(self):
        raise TypeError("Field does not support implicit conversion to bool")

    def __bool__(self):
        raise TypeError("Field does not support implicit conversion to bool")

67
    @staticmethod
68
    def full(domain, val):
Martin Reinecke's avatar
Martin Reinecke committed
69
70
71
72
73
74
75
76
77
78
79
80
81
82
        """Creates a Field with a given domain, filled with a constant value.

        Parameters
        ----------
        domain : Domain, tuple of Domain, or DomainTuple
            domain of the new Field
        val : float/complex/int scalar
            fill value. Data type of the field is inferred from val.

        Returns
        -------
        Field
            the newly created field
        """
83
84
        if not np.isscalar(val):
            raise TypeError("val must be a scalar")
85
86
87
88
        if not (np.isreal(val) or np.iscomplex(val)):
            raise TypeError("need arithmetic scalar")
        domain = DomainTuple.make(domain)
        return Field(domain, dobj.full(domain.shape, fill_value=val))
89

90
    @staticmethod
91
    def from_global_data(domain, arr, sum_up=False):
Martin Reinecke's avatar
Martin Reinecke committed
92
93
94
95
96
97
98
99
100
        """Returns a Field constructed from `domain` and `arr`.

        Parameters
        ----------
        domain : DomainTuple, tuple of Domain, or Domain
            the domain of the new Field
        arr : numpy.ndarray
            The data content to be used for the new Field.
            Its shape must match the shape of `domain`.
101
102
103
104
105
        sum_up : bool, optional
            If True, the contents of `arr` are summed up over all MPI tasks
            (if any), and the sum is used as data content.
            If False, the contens of `arr` are used directly, and must be
            identical on all MPI tasks.
Martin Reinecke's avatar
Martin Reinecke committed
106
        """
107
108
        return Field(DomainTuple.make(domain),
                     dobj.from_global_data(arr, sum_up))
109

Martin Reinecke's avatar
Martin Reinecke committed
110
111
    @staticmethod
    def from_local_data(domain, arr):
112
        return Field(DomainTuple.make(domain),
Martin Reinecke's avatar
Martin Reinecke committed
113
                     dobj.from_local_data(domain.shape, arr))
Martin Reinecke's avatar
Martin Reinecke committed
114

115
    def to_global_data(self):
Martin Reinecke's avatar
Martin Reinecke committed
116
117
118
119
120
121
122
123
124
125
126
127
        """Returns an array containing the full data of the field.

        Returns
        -------
        numpy.ndarray : array containing all field entries.
            Its shape is identical to `self.shape`.

        Notes
        -----
        Do not write to the returned array! Depending on whether MPI is
        active or not, this may or may not change the field's data content.
        """
128
129
        return dobj.to_global_data(self._val)

Martin Reinecke's avatar
Martin Reinecke committed
130
131
    @property
    def local_data(self):
Martin Reinecke's avatar
Martin Reinecke committed
132
133
134
135
136
        """numpy.ndarray : locally residing field data

        Returns a handle to the part of the array data residing on the local
        task (or to the entore array if MPI is not active).
        """
Martin Reinecke's avatar
Martin Reinecke committed
137
138
        return dobj.local_data(self._val)

Martin Reinecke's avatar
Martin Reinecke committed
139
    def cast_domain(self, new_domain):
Martin Reinecke's avatar
Martin Reinecke committed
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
        """Returns a field with the same data, but a different domain

        Parameters
        ----------
        new_domain : Domain, tuple of Domain, or DomainTuple
            The domain for the returned field. Must be shape-compatible to
            `self`.

        Returns
        -------
        Field
            Field living on `new_domain`, but with the same data as `self`.

        Notes
        -----
        No copy is made. If needed, use an additional copy() invocation.
        """
157
        return Field(DomainTuple.make(new_domain), self._val)
158

Martin Reinecke's avatar
Martin Reinecke committed
159
160
    @staticmethod
    def from_random(random_type, domain, dtype=np.float64, **kwargs):
161
162
163
164
        """ Draws a random field with the given parameters.

        Parameters
        ----------
Martin Reinecke's avatar
Martin Reinecke committed
165
166
        random_type : 'pm1', 'normal', or 'uniform'
            The random distribution to use.
Martin Reinecke's avatar
Martin Reinecke committed
167
        domain : DomainTuple
168
169
170
            The domain of the output random field
        dtype : type
            The datatype of the output random field
Theo Steininger's avatar
Theo Steininger committed
171

172
173
        Returns
        -------
Martin Reinecke's avatar
Martin Reinecke committed
174
        Field
Martin Reinecke's avatar
Martin Reinecke committed
175
            The newly created Field.
176
        """
Martin Reinecke's avatar
Martin Reinecke committed
177
        domain = DomainTuple.make(domain)
Martin Reinecke's avatar
Martin Reinecke committed
178
179
180
        return Field(domain=domain,
                     val=dobj.from_random(random_type, dtype=dtype,
                                          shape=domain.shape, **kwargs))
181

Theo Steininger's avatar
Theo Steininger committed
182
183
    @property
    def val(self):
Martin Reinecke's avatar
Martin Reinecke committed
184
185
186
187
188
189
        """dobj.data_object : the data object storing the field's entries

        Notes
        -----
        This property is intended for low-level, internal use only. Do not use
        from outside of NIFTy's core; there should be better alternatives.
190
        """
Martin Reinecke's avatar
Martin Reinecke committed
191
        return self._val
csongor's avatar
csongor committed
192

Martin Reinecke's avatar
Martin Reinecke committed
193
194
    @property
    def dtype(self):
Martin Reinecke's avatar
Martin Reinecke committed
195
        """type : the data type of the field's entries"""
Martin Reinecke's avatar
Martin Reinecke committed
196
197
        return self._val.dtype

Martin Reinecke's avatar
Martin Reinecke committed
198
199
    @property
    def domain(self):
Martin Reinecke's avatar
Martin Reinecke committed
200
        """DomainTuple : the field's domain"""
Martin Reinecke's avatar
Martin Reinecke committed
201
202
        return self._domain

203
204
    @property
    def shape(self):
Martin Reinecke's avatar
Martin Reinecke committed
205
        """tuple of int : the concatenated shapes of all sub-domains"""
Martin Reinecke's avatar
Martin Reinecke committed
206
        return self._domain.shape
csongor's avatar
csongor committed
207

208
    @property
Martin Reinecke's avatar
Martin Reinecke committed
209
    def size(self):
Martin Reinecke's avatar
Martin Reinecke committed
210
        """int : total number of pixels in the field"""
Martin Reinecke's avatar
Martin Reinecke committed
211
        return self._domain.size
csongor's avatar
csongor committed
212

Theo Steininger's avatar
Theo Steininger committed
213
214
    @property
    def real(self):
Martin Reinecke's avatar
Martin Reinecke committed
215
        """Field : The real part of the field"""
216
        if not np.issubdtype(self.dtype, np.complexfloating):
217
            return self
Martin Reinecke's avatar
Martin Reinecke committed
218
        return Field(self._domain, self._val.real)
Theo Steininger's avatar
Theo Steininger committed
219
220
221

    @property
    def imag(self):
Martin Reinecke's avatar
Martin Reinecke committed
222
        """Field : The imaginary part of the field"""
223
224
        if not np.issubdtype(self.dtype, np.complexfloating):
            raise ValueError(".imag called on a non-complex Field")
Martin Reinecke's avatar
Martin Reinecke committed
225
        return Field(self._domain, self._val.imag)
Theo Steininger's avatar
Theo Steininger committed
226

227
    def scalar_weight(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
228
229
230
231
232
233
234
235
236
237
238
239
240
241
        """Returns the uniform volume element for a sub-domain of `self`.

        Parameters
        ----------
        spaces : int, tuple of int or None
            indices of the sub-domains of the field's domain to be considered.
            If `None`, the entire domain is used.

        Returns
        -------
        float or None
            if the requested sub-domain has a uniform volume element, it is
            returned. Otherwise, `None` is returned.
        """
242
        if np.isscalar(spaces):
Martin Reinecke's avatar
Martin Reinecke committed
243
            return self._domain[spaces].scalar_dvol
244
245

        if spaces is None:
Martin Reinecke's avatar
Martin Reinecke committed
246
            spaces = range(len(self._domain))
Martin Reinecke's avatar
Martin Reinecke committed
247
        res = 1.
248
        for i in spaces:
Martin Reinecke's avatar
Martin Reinecke committed
249
            tmp = self._domain[i].scalar_dvol
250
251
252
253
254
            if tmp is None:
                return None
            res *= tmp
        return res

Martin Reinecke's avatar
Martin Reinecke committed
255
    def total_volume(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
256
257
258
259
260
261
262
263
264
265
266
267
268
        """Returns the total volume of a sub-domain of `self`.

        Parameters
        ----------
        spaces : int, tuple of int or None
            indices of the sub-domains of the field's domain to be considered.
            If `None`, the entire domain is used.

        Returns
        -------
        float
            the total volume of the requested sub-domain.
        """
Martin Reinecke's avatar
Martin Reinecke committed
269
        if np.isscalar(spaces):
Martin Reinecke's avatar
Martin Reinecke committed
270
            return self._domain[spaces].total_volume
Martin Reinecke's avatar
Martin Reinecke committed
271
272
273
274
275

        if spaces is None:
            spaces = range(len(self._domain))
        res = 1.
        for i in spaces:
Martin Reinecke's avatar
Martin Reinecke committed
276
            res *= self._domain[i].total_volume
Martin Reinecke's avatar
Martin Reinecke committed
277
278
        return res

279
    def weight(self, power=1, spaces=None):
Theo Steininger's avatar
Theo Steininger committed
280
        """ Weights the pixels of `self` with their invidual pixel-volume.
281
282
283
284

        Parameters
        ----------
        power : number
Theo Steininger's avatar
Theo Steininger committed
285
            The pixels get weighted with the volume-factor**power.
Theo Steininger's avatar
Theo Steininger committed
286

Martin Reinecke's avatar
Martin Reinecke committed
287
288
289
        spaces : None, int or tuple of int
            Determines on which sub-domain the operation takes place.
            If None, the entire domain is used.
Theo Steininger's avatar
Theo Steininger committed
290

291
292
        Returns
        -------
Martin Reinecke's avatar
Martin Reinecke committed
293
        Field
Theo Steininger's avatar
Theo Steininger committed
294
            The weighted field.
295
        """
296
        aout = self.local_data.copy()
csongor's avatar
csongor committed
297

Martin Reinecke's avatar
Martin Reinecke committed
298
        spaces = utilities.parse_spaces(spaces, len(self._domain))
csongor's avatar
csongor committed
299

300
301
        fct = 1.
        for ind in spaces:
Martin Reinecke's avatar
Martin Reinecke committed
302
            wgt = self._domain[ind].dvol
303
304
305
            if np.isscalar(wgt):
                fct *= wgt
            else:
Martin Reinecke's avatar
Martin Reinecke committed
306
                new_shape = np.ones(len(self.shape), dtype=np.int)
Martin Reinecke's avatar
Martin Reinecke committed
307
308
                new_shape[self._domain.axes[ind][0]:
                          self._domain.axes[ind][-1]+1] = wgt.shape
309
                wgt = wgt.reshape(new_shape)
Martin Reinecke's avatar
Martin Reinecke committed
310
311
                if dobj.distaxis(self._val) >= 0 and ind == 0:
                    # we need to distribute the weights along axis 0
Martin Reinecke's avatar
fixes  
Martin Reinecke committed
312
                    wgt = dobj.local_data(dobj.from_global_data(wgt))
313
                aout *= wgt**power
314
        fct = fct**power
Martin Reinecke's avatar
Martin Reinecke committed
315
        if fct != 1.:
316
            aout *= fct
317

318
        return Field.from_local_data(self._domain, aout)
csongor's avatar
csongor committed
319

Martin Reinecke's avatar
Martin Reinecke committed
320
    def vdot(self, x=None, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
321
        """ Computes the dot product of 'self' with x.
Theo Steininger's avatar
Theo Steininger committed
322

323
324
325
        Parameters
        ----------
        x : Field
326
            x must live on the same domain as `self`.
Theo Steininger's avatar
Theo Steininger committed
327

Martin Reinecke's avatar
Martin Reinecke committed
328
        spaces : None, int or tuple of int (default: None)
329
330
            The dot product is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.
Theo Steininger's avatar
Theo Steininger committed
331

332
333
        Returns
        -------
Martin Reinecke's avatar
Martin Reinecke committed
334
        float, complex, either scalar (for full dot products)
335
                              or Field (for partial dot products)
336
        """
337
        if not isinstance(x, Field):
338
339
            raise TypeError("The dot-partner must be an instance of " +
                            "the NIFTy field class")
Theo Steininger's avatar
Theo Steininger committed
340

341
        if x._domain is not self._domain:
342
            raise ValueError("Domain mismatch")
Theo Steininger's avatar
Theo Steininger committed
343

Martin Reinecke's avatar
Martin Reinecke committed
344
        ndom = len(self._domain)
345
346
347
        spaces = utilities.parse_spaces(spaces, ndom)

        if len(spaces) == ndom:
Martin Reinecke's avatar
Martin Reinecke committed
348
            return dobj.vdot(self._val, x._val)
349
350
        # If we arrive here, we have to do a partial dot product.
        # For the moment, do this the explicit, non-optimized way
Martin Reinecke's avatar
Martin Reinecke committed
351
        return (self.conjugate()*x).sum(spaces=spaces)
Theo Steininger's avatar
Theo Steininger committed
352

Theo Steininger's avatar
Theo Steininger committed
353
    def norm(self):
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
354
        """ Computes the L2-norm of the field values.
csongor's avatar
csongor committed
355

Theo Steininger's avatar
Theo Steininger committed
356
357
        Returns
        -------
Martin Reinecke's avatar
Martin Reinecke committed
358
        float
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
359
            The L2-norm of the field values.
csongor's avatar
csongor committed
360
        """
361
        return np.sqrt(abs(self.vdot(x=self)))
csongor's avatar
csongor committed
362

363
364
365
366
367
368
369
370
371
372
    def squared_norm(self):
        """ Computes the square of the L2-norm of the field values.

        Returns
        -------
        float
            The square of the L2-norm of the field values.
        """
        return abs(self.vdot(x=self))

Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
373
    def conjugate(self):
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
374
        """ Returns the complex conjugate of the field.
Theo Steininger's avatar
Theo Steininger committed
375

376
377
        Returns
        -------
Martin Reinecke's avatar
Martin Reinecke committed
378
379
        Field
            The complex conjugated field.
csongor's avatar
csongor committed
380
        """
Martin Reinecke's avatar
Martin Reinecke committed
381
        return Field(self._domain, self._val.conjugate())
csongor's avatar
csongor committed
382

Theo Steininger's avatar
Theo Steininger committed
383
    # ---General unary/contraction methods---
384

Theo Steininger's avatar
Theo Steininger committed
385
    def __pos__(self):
386
        return self
387

Theo Steininger's avatar
Theo Steininger committed
388
    def __neg__(self):
Martin Reinecke's avatar
Martin Reinecke committed
389
        return Field(self._domain, -self._val)
csongor's avatar
csongor committed
390

Theo Steininger's avatar
Theo Steininger committed
391
    def __abs__(self):
Martin Reinecke's avatar
Martin Reinecke committed
392
        return Field(self._domain, abs(self._val))
csongor's avatar
csongor committed
393

394
    def _contraction_helper(self, op, spaces):
Theo Steininger's avatar
Theo Steininger committed
395
        if spaces is None:
Martin Reinecke's avatar
Martin Reinecke committed
396
            return getattr(self._val, op)()
397

Martin Reinecke's avatar
Martin Reinecke committed
398
        spaces = utilities.parse_spaces(spaces, len(self._domain))
csongor's avatar
csongor committed
399

Martin Reinecke's avatar
Martin Reinecke committed
400
        axes_list = tuple(self._domain.axes[sp_index] for sp_index in spaces)
401

Martin Reinecke's avatar
Martin Reinecke committed
402
        if len(axes_list) > 0:
Theo Steininger's avatar
Theo Steininger committed
403
            axes_list = reduce(lambda x, y: x+y, axes_list)
csongor's avatar
csongor committed
404

Martin Reinecke's avatar
stage1  
Martin Reinecke committed
405
        # perform the contraction on the data
Martin Reinecke's avatar
Martin Reinecke committed
406
        data = getattr(self._val, op)(axis=axes_list)
csongor's avatar
csongor committed
407

Theo Steininger's avatar
Theo Steininger committed
408
409
410
        # 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
411
        else:
Martin Reinecke's avatar
Martin Reinecke committed
412
            return_domain = tuple(dom
Martin Reinecke's avatar
Martin Reinecke committed
413
                                  for i, dom in enumerate(self._domain)
Theo Steininger's avatar
Theo Steininger committed
414
                                  if i not in spaces)
415

416
            return Field(DomainTuple.make(return_domain), data)
csongor's avatar
csongor committed
417

418
    def sum(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
419
420
421
422
423
424
425
426
427
428
429
430
431
432
        """Sums up over the sub-domains given by `spaces`.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The summation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the summation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
433
        return self._contraction_helper('sum', spaces)
csongor's avatar
csongor committed
434

435
    def integrate(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
        """Integrates over the sub-domains given by `spaces`.

        Integration is performed by summing over `self` multiplied by its
        volume factors.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The summation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the integration. If it is carried out over the
            entire domain, this is a scalar, otherwise a Field.
        """
Martin Reinecke's avatar
Martin Reinecke committed
453
454
455
456
457
        swgt = self.scalar_weight(spaces)
        if swgt is not None:
            res = self.sum(spaces)
            res *= swgt
            return res
458
459
460
        tmp = self.weight(1, spaces=spaces)
        return tmp.sum(spaces)

461
    def prod(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
462
463
464
465
466
467
468
469
470
471
472
473
474
475
        """Computes the product over the sub-domains given by `spaces`.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the product. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
476
        return self._contraction_helper('prod', spaces)
csongor's avatar
csongor committed
477

478
479
    def all(self, spaces=None):
        return self._contraction_helper('all', spaces)
csongor's avatar
csongor committed
480

481
482
    def any(self, spaces=None):
        return self._contraction_helper('any', spaces)
csongor's avatar
csongor committed
483

484
    def min(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
485
486
487
488
489
490
491
492
493
494
495
496
497
498
        """Determines the minimum over the sub-domains given by `spaces`.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the operation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
499
        return self._contraction_helper('min', spaces)
csongor's avatar
csongor committed
500

501
    def max(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
502
503
504
505
506
507
508
509
510
511
512
513
514
515
        """Determines the maximum over the sub-domains given by `spaces`.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the operation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
516
        return self._contraction_helper('max', spaces)
csongor's avatar
csongor committed
517

518
    def mean(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
        """Determines the mean over the sub-domains given by `spaces`.

        ``x.mean(spaces)`` is equivalent to
        ``x.integrate(spaces)/x.total_volume(spaces)``.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the operation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
536
537
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('mean', spaces)
Martin Reinecke's avatar
Martin Reinecke committed
538
        # MR FIXME: not very efficient
539
540
        # MR FIXME: do we need "spaces" here?
        tmp = self.weight(1, spaces)
Martin Reinecke's avatar
Martin Reinecke committed
541
        return tmp.sum(spaces)*(1./tmp.total_volume(spaces))
csongor's avatar
csongor committed
542

543
    def var(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
544
545
546
547
548
549
550
551
552
553
554
555
556
557
        """Determines the variance over the sub-domains given by `spaces`.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the operation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
558
559
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('var', spaces)
Martin Reinecke's avatar
Martin Reinecke committed
560
561
562
        # MR FIXME: not very efficient or accurate
        m1 = self.mean(spaces)
        if np.issubdtype(self.dtype, np.complexfloating):
563
            sq = abs(self-m1)**2
Martin Reinecke's avatar
Martin Reinecke committed
564
        else:
565
566
            sq = (self-m1)**2
        return sq.mean(spaces)
csongor's avatar
csongor committed
567

568
    def std(self, spaces=None):
Martin Reinecke's avatar
Martin Reinecke committed
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
        """Determines the standard deviation over the sub-domains given by
        `spaces`.

        ``x.std(spaces)`` is equivalent to ``sqrt(x.var(spaces))``.

        Parameters
        ----------
        spaces : None, int or tuple of int (default: None)
            The operation is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        Field or scalar
            The result of the operation. If it is carried out over the entire
            domain, this is a scalar, otherwise a Field.
        """
586
        from .sugar import sqrt
587
588
589
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('std', spaces)
        return sqrt(self.var(spaces))
csongor's avatar
csongor committed
590

Theo Steininger's avatar
Theo Steininger committed
591
    def __repr__(self):
Philipp Arras's avatar
Philipp Arras committed
592
        return "<nifty5.Field>"
Theo Steininger's avatar
Theo Steininger committed
593
594

    def __str__(self):
Philipp Arras's avatar
Philipp Arras committed
595
        return "nifty5.Field instance\n- domain      = " + \
596
               self._domain.__str__() + \
Martin Reinecke's avatar
Martin Reinecke committed
597
               "\n- val         = " + repr(self._val)
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
598

599
600
601
    def isEquivalentTo(self, other):
        """Determines (as quickly as possible) whether `self`'s content is
        identical to `other`'s content."""
602
603
604
605
        if self is other:
            return True
        if not isinstance(other, Field):
            return False
606
        if self._domain is not other._domain:
607
608
609
            return False
        return (self._val == other._val).all()

610
611
612
613
614
    def isSubsetOf(self, other):
        """Identical to `Field.isEquivalentTo()`. This method is provided for
        easier interoperability with `MultiField`."""
        return self.isEquivalentTo(other)

615

616
617
618
619
620
621
622
for op in ["__add__", "__radd__",
           "__sub__", "__rsub__",
           "__mul__", "__rmul__",
           "__div__", "__rdiv__",
           "__truediv__", "__rtruediv__",
           "__floordiv__", "__rfloordiv__",
           "__pow__", "__rpow__",
623
624
625
           "__lt__", "__le__", "__gt__", "__ge__", "__eq__", "__ne__"]:
    def func(op):
        def func2(self, other):
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
626
627
            # if other is a field, make sure that the domains match
            if isinstance(other, Field):
628
                if other._domain is not self._domain:
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
629
                    raise ValueError("domains are incompatible.")
Martin Reinecke's avatar
Martin Reinecke committed
630
                tval = getattr(self._val, op)(other._val)
631
                return Field(self._domain, tval)
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
632

Martin Reinecke's avatar
fix  
Martin Reinecke committed
633
634
            if (np.isscalar(other) or
                    isinstance(other, (dobj.data_object, np.ndarray))):
Martin Reinecke's avatar
Martin Reinecke committed
635
                tval = getattr(self._val, op)(other)
636
                return Field(self._domain, tval)
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
637

Martin Reinecke's avatar
fix  
Martin Reinecke committed
638
            raise TypeError("should not arrive here")
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
639
            return NotImplemented
640
641
        return func2
    setattr(Field, op, func(op))
642
643
644
645
646
647
648
649
650

for op in ["__iadd__", "__isub__", "__imul__", "__idiv__",
           "__itruediv__", "__ifloordiv__", "__ipow__"]:
    def func(op):
        def func2(self, other):
            raise TypeError(
                "In-place operations are deliberately not supported")
        return func2
    setattr(Field, op, func(op))