core.py 65 KB
Newer Older
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
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
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
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
316
317
318
319
320
321
322
323
324
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
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
#!/usr/bin/env
# encoding: utf-8
"""
Author:     Daniel Boeckenhoff
Mail:       daniel.boeckenhoff@ipp.mpg.de

core of tfields library
contains numpy ndarray derived bases of the tfields package
"""
import warnings
import os
import pathlib
from six import string_types
from contextlib import contextmanager
from collections import Counter

import numpy as np
import sympy
import scipy as sp
import tfields.bases
np.seterr(all='warn', over='raise')


def rank(tensor):
    """
    Tensor rank
    """
    return len(tensor.shape) - 1


def dim(tensor):
    """
    Manifold dimension
    """
    if rank(tensor) == 0:
        return 1
    return tensor.shape[1]


class AbstractNdarray(np.ndarray):
    """
    All tensors and subclasses should derive from AbstractNdarray.
    AbstractNdarray implements all the inheritance specifics for np.ndarray
    Whene inheriting, three attributes are of interest:
        __slots__ (list of str): If you want to add attributes to
            your AbstractNdarray subclass, add the attribute name to __slots__
        __slot_defaults__ (list): if __slot_defaults__ is None, the
            defaults for the attributes in __slots__ will be None
            other values will be treaded as defaults to the corresponding
            arg at the same position in the __slots__ list.
        __slotDtype__ (list of types): for the conversion of the
            args in __slots__ to numpy arrays. None values mean no
            conversion.

    Args:
        array (array-like): input array
        **kwargs: arguments corresponding to __slots__
    TODO:
        equality check
    """
    __slots__ = []
    __slot_defaults__ = []
    __slotDtypes__ = []
    __slot_setters__ = []

    def __new__(cls, array, **kwargs):  # pragma: no cover
        raise NotImplementedError("{clsType} type must implement '__new__'"
                                  .format(clsType=type(cls)))

    def __array_finalize__(self, obj):
        if obj is None:
            return
        for attr in self._iter_slots():
            setattr(self, attr, getattr(obj, attr, None))

    def __array_wrap__(self, out_arr, context=None):
        return np.ndarray.__array_wrap__(self, out_arr, context)

    @classmethod
    def _iter_slots(cls):
        return [att for att in cls.__slots__ if att != '_cache']

    @classmethod
    def _update_slot_kwargs(cls, kwargs):
        """
        set the defaults in kwargs according to __slot_defaults__
        and convert the kwargs according to __slotDtypes__
        """
        slotDefaults = cls.__slot_defaults__ + \
            [None] * (len(cls.__slots__) - len(cls.__slot_defaults__))
        slotDtypes = cls.__slotDtypes__ + \
            [None] * (len(cls.__slots__) - len(cls.__slotDtypes__))
        for attr, default, dtype in zip(cls.__slots__, slotDefaults, slotDtypes):
            if attr == '_cache':
                continue
            if attr not in kwargs:
                kwargs[attr] = default
            if dtype is not None:
                try:
                    kwargs[attr] = np.array(kwargs[attr], dtype=dtype)
                except Exception as err:
                    raise ValueError(str(attr) + str(dtype) + str(kwargs[attr]) + str(err))

    def __setattr__(self, name, value):
        if name in self.__slots__:
            index = self.__slots__.index(name)
            try:
                setter = self.__slot_setters__[index]
            except IndexError:
                setter = None
            if setter is not None:
                value = setter(value)
        super(AbstractNdarray, self).__setattr__(name, value)

    def __reduce__(self):
        """
        important for pickling
        Examples:
            >>> from tempfile import NamedTemporaryFile
            >>> import pickle
            >>> import tfields

            Build a dummy scalar field
            >>> from tfields import Tensors, TensorFields
            >>> scalars = Tensors([0, 1, 2])
            >>> vectors = Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
            >>> scalarField = TensorFields(vectors, scalars, coordSys='cylinder')

            Save it and restore it
            >>> outFile = NamedTemporaryFile(suffix='.pickle')

            >>> pickle.dump(scalarField,
            ...             outFile)
            >>> _ = outFile.seek(0)

            >>> sf = pickle.load(outFile)
            >>> sf.coordSys == 'cylinder'
            True
            >>> sf.fields[0][2] == 2.
            True

        """
        # Get the parent's __reduce__ tuple
        pickled_state = super(AbstractNdarray, self).__reduce__()

        # Create our own tuple to pass to __setstate__
        new_state = pickled_state[2] + tuple([getattr(self, slot) for slot in
                                              self._iter_slots()])

        # Return a tuple that replaces the parent's __setstate__ tuple with our own
        return (pickled_state[0], pickled_state[1], new_state)

    def __setstate__(self, state):
        """
        important for unpickling
        """
        # Call the parent's __setstate__ with the other tuple elements.
        super(AbstractNdarray, self).__setstate__(state[0:-len(self._iter_slots())])

        # set the __slot__ attributes
        for i, slot in enumerate(reversed(self._iter_slots())):
            index = -(i + 1)
            setattr(self, slot, state[index])

    def copy(self, *args, **kwargs):
        """
        The standard ndarray copy does not copy slots. Correct for this.
        Examples:
            >>> import tfields
            >>> m = tfields.TensorMaps([[1,2,3], [3,3,3], [0,0,0], [5,6,7]],
            ...                        maps=[tfields.TensorFields([[0, 1, 2], [1, 2, 3]],
            ...                                                   [1, 2])])
            >>> mc = m.copy()
            >>> mc is m
            False
            >>> mc.maps[0].fields[0] is m.maps[0].fields[0]
            False

        TODO: This function implementation could be more general or maybe redirect to deepcopy?
        """
        inst = super(AbstractNdarray, self).copy(*args, **kwargs)
        for attr in self._iter_slots():
            value = getattr(self, attr)
            if hasattr(value, 'copy'):
                setattr(inst, attr, value.copy(*args, **kwargs))
            elif isinstance(value, list):
                list_copy = []
                for item in value:
                    if hasattr(item, 'copy'):
                        list_copy.append(item.copy(*args, **kwargs))
                    else:
                        list_copy.append(item)
                setattr(inst, attr, list_copy)

        return inst

    def save(self, path, *args, **kwargs):
        """
        Saving a tensors object by redirecting to the correct save method depending on path
        Args:
            path (str or buffer)
            *args:
                forwarded to extension specific method
            **kwargs:
                extension (str): only needed if path is buffer
                ... remaining:forwarded to extension specific method
        """
        # get the extension
        if isinstance(path, string_types):
            extension = pathlib.Path(path).suffix.lstrip('.')

        # get the save method
        try:
            save_method = getattr(self,
                                  '_save_{extension}'.format(**locals()))
        except:
            raise NotImplementedError("Can not find save method for extension: "
                                      "{extension}.".format(**locals()))

        # resolve:     relative paths,  symlinks and    ~
        path = os.path.realpath(os.path.abspath(os.path.expanduser(path)))
        return save_method(path, **kwargs)

    @classmethod
    def load(cls, path, *args, **kwargs):
        """
        load a file as a tensors object.
        Args:
            path (str or buffer)
            *args:
                forwarded to extension specific method
            **kwargs:
                extension (str): only needed if path is buffer
                ... remaining:forwarded to extension specific method
        """
        extension = kwargs.pop('extension', 'npz')
        if isinstance(path, string_types):
            path = os.path.realpath(os.path.abspath(os.path.expanduser(path)))
            extension = pathlib.Path(path).suffix.lstrip('.')

        try:
            load_method = getattr(cls, '_load_{e}'.format(e=extension))
        except:
            raise NotImplementedError("Can not find load method for extension: "
                                      "{extension}.".format(**locals()))
        return load_method(path, *args, **kwargs)

    def _save_npz(self, path, **kwargs):
        """
        Args:
            path (open file or str/unicode): destination to save file to.
        Examples:
            >>> import tfields
            >>> from tempfile import NamedTemporaryFile
            >>> outFile = NamedTemporaryFile(suffix='.npz')
            >>> p = tfields.Points3D([[1., 2., 3.], [4., 5., 6.], [1, 2, -6]])
            >>> p.save(outFile.name)
            >>> _ = outFile.seek(0)
            >>> p1 = tfields.Points3D.load(outFile.name)
            >>> assert p.equal(p1)

        """
        kwargs = {}
        for attr in self._iter_slots():
            if not hasattr(self, attr):
                # attribute in __slots__ not found.
                warnings.warn("When saving instance of class {0} Attribute {1} not set."
                              "This Attribute is not saved.".format(self.__class__, attr), Warning)
            else:
                kwargs[attr] = getattr(self, attr)

        np.savez(path, self, **kwargs)

    @classmethod
    def _load_npz(cls, path, **load_kwargs):
        """
        Factory method
        Given a path to a npz file, construct the object
        """
        np_file = np.load(path, **load_kwargs)
        keys = np_file.keys()
        bulk = np_file['arr_0']
        data_kwargs = {key: np_file[key] for key in keys if key not in ['arr_0']}
        return cls.__new__(cls, bulk, **data_kwargs)


class Tensors(AbstractNdarray):
    """
    Set of tensors with the same basis.
    TODO:
        all slot args should be protected -> _base
    Args:
        tensors: np.ndarray or AbstractNdarray subclass
    Examples:
        >>> import numpy as np

        Initialize a scalar range
        >>> scalars = tfields.Tensors([0, 1, 2])
        >>> scalars.rank == 0
        True

        Initialize vectors
        >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
        >>> vectors.rank == 1
        True
        >>> vectors.dim == 3
        True
        >>> assert vectors.coordSys == 'cartesian'

        Initialize the Levi-Zivita Tensor
        >>> matrices = tfields.Tensors([[[0, 0, 0], [0, 0, 1], [0, -1, 0]],
        ...                     [[0, 0, -1], [0, 0, 0], [1, 0, 0]],
        ...                     [[0, 1, 0], [-1, 0, 0], [0, 0, 0]]])
        >>> matrices.shape == (3, 3, 3)
        True
        >>> matrices.rank == 2
        True
        >>> matrices.dim == 3
        True

        Initializing in different start coordinate system
        >>> cyl = tfields.Tensors([[5, np.arctan(4. / 3.), 42]], coordSys='cylinder')
        >>> assert cyl.coordSys == 'cylinder'
        >>> cyl.transform('cartesian')
        >>> assert cyl.coordSys == 'cartesian'
        >>> cart = cyl
        >>> assert round(cart[0, 0], 10) == 3.
        >>> assert round(cart[0, 1], 10) == 4.
        >>> assert cart[0, 2] == 42

        Initialize with copy constructor keeps the coordinate system
        >>> with vectors.tmp_transform('cylinder'):
        ...     vect_cyl = tfields.Tensors(vectors)
        ...     assert vect_cyl.coordSys == vectors.coordSys
        >>> assert vect_cyl.coordSys == 'cylinder'

        You can demand a special dimension.
        >>> _ = tfields.Tensors([[1, 2, 3]], dim=3)
        >>> _ = tfields.Tensors([[1, 2, 3]], dim=2)  # doctest: +ELLIPSIS
        Traceback (most recent call last):
            ...
        ValueError: Incorrect dimension: 3 given, 2 demanded.

        The dimension argument (dim) becomes necessary if you want to initialize
        an empty array
        >>> _ = tfields.Tensors([])  # doctest: +ELLIPSIS
        Traceback (most recent call last):
            ...
        ValueError: Empty tensors need dimension parameter 'dim'.
        >>> tfields.Tensors([], dim=7)
        Tensors([], shape=(0, 7), dtype=float64)

    """
    __slots__ = ['coordSys']
    __slot_defaults__ = ['cartesian']
    __slot_setters__ = [tfields.bases.get_coord_system_name]

    def __new__(cls, tensors, **kwargs):
        dtype = kwargs.pop('dtype', None)
        order = kwargs.pop('order', None)
        dim = kwargs.pop('dim', None)

        ''' copy constructor extracts the kwargs from tensors'''
        if issubclass(type(tensors), Tensors):
            if dim is not None:
                dim = tensors.dim
            coordSys = kwargs.pop('coordSys', tensors.coordSys)
            tensors = tensors.copy()
            tensors.transform(coordSys)
            kwargs['coordSys'] = coordSys
            if dtype is None:
                dtype = tensors.dtype
        else:
            if dtype is None:
                dtype = np.float64

        ''' demand iterable structure '''
        try:
            len(tensors)
        except TypeError as err:
            raise TypeError("Iterable structure necessary."
                            " Got {tensors}"
                            .format(**locals()))

        ''' process empty inputs '''
        if len(tensors) == 0:
            if issubclass(type(tensors), tfields.Tensors):
                tensors = np.empty(tensors.shape, dtype=tensors.dtype)
            elif dim is not None:
                tensors = np.empty((0, dim))
            if issubclass(type(tensors), np.ndarray):
                # np.empty
                pass
            else:
                raise ValueError("Empty tensors need dimension "
                                 "parameter 'dim'.")

        tensors = np.asarray(tensors, dtype=dtype, order=order)
        obj = tensors.view(cls)

        ''' check dimension(s) '''
        for d in obj.shape[1:]:
            if not d == obj.dim:
                raise ValueError("Dimensions are inconstistent. "
                                 "Manifold dimension is {obj.dim}, "
                                 "Found dimensions {found} in {obj}."
                                 .format(found=obj.shape[1:], **locals()))
        if dim is not None:
            if dim != obj.dim:
                raise ValueError("Incorrect dimension: {obj.dim} given,"
                                 " {dim} demanded."
                                 .format(**locals()))

        ''' update kwargs with defaults from slots '''
        cls._update_slot_kwargs(kwargs)

        ''' set kwargs to slots attributes '''
        for attr in kwargs:
            if attr not in cls._iter_slots():
                raise AttributeError("Keyword argument {attr} not accepted "
                                     "for class {cls}".format(**locals()))
            setattr(obj, attr, kwargs[attr])

        return obj

    @classmethod
    def merged(cls, *objects, **kwargs):
        """
        Factory method
        Merges all tensor inputs to one tensor

        Examples:
            >>> import numpy as np
            >>> import tfields
            >>> import tfields.bases

            Use of most frequent coordinate system
            >>> vec_a = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
            >>> vec_b = tfields.Tensors([[5, 4, 1]], coordSys=tfields.bases.cylinder)
            >>> vec_c = tfields.Tensors([[4, 2, 3]], coordSys=tfields.bases.cylinder)
            >>> merge = tfields.Tensors.merged(vec_a, vec_b, vec_c, [[2, 0, 1]])
            >>> assert merge.coordSys == 'cylinder'
            >>> assert merge.equal([[0, 0, 0],
            ...                     [0, 0, 1],
            ...                     [1, -np.pi / 2, 0],
            ...                     [5, 4, 1],
            ...                     [4, 2, 3],
            ...                     [2, 0, 1]])

            Merge also shifts the maps to still refer to the same tensors
            >>> tm_a = tfields.TensorMaps(merge, maps=[[[0, 1, 2]]])
            >>> tm_b = tm_a.copy()
            >>> assert tm_a.coordSys == 'cylinder'
            >>> tm_merge = tfields.TensorMaps.merged(tm_a, tm_b)
            >>> assert tm_merge.coordSys == 'cylinder'
            >>> assert tm_merge.maps[0].equal([[0, 1, 2],
            ...                               list(range(len(merge),
            ...                                          len(merge) + 3,
            ...                                          1))])
            
            >>> obj_list = [tfields.Tensors([[1, 2, 3]], coordSys=tfields.bases.CYLINDER),
            ...             tfields.Tensors([[3] * 3]),
            ...             tfields.Tensors([[5, 1, 3]])]
            >>> merge2 = tfields.Tensors.merged(*obj_list, coordSys=tfields.bases.CARTESIAN)
            >>> assert merge2.equal([[-0.41614684, 0.90929743, 3.],
            ...                      [3, 3, 3], [5, 1, 3]], atol=1e-8)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
467

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
        """

        ''' get most frequent coordSys or predefined coordSys '''
        coordSys = kwargs.get('coordSys', None)
        dimension = kwargs.get('dim', None)
        if coordSys is None:
            bases = []
            for t in objects:
                try:
                    bases.append(t.coordSys)
                except AttributeError:
                    pass
            if bases:
                # get most frequent coordSys
                coordSys = sorted(bases, key=Counter(bases).get, reverse=True)[0]
                kwargs['coordSys'] = coordSys
            else:
                default = cls.__slot_defaults__[cls.__slots__.index('coordSys')]
                kwargs['coordSys'] = default

        ''' transform all raw inputs to cls type with correct coordSys. Also
        automatically make a copy of those instances that are of the correct
        type already.'''
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
491
        objects = [cls.__new__(cls, t, **kwargs) for t in objects]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689

        ''' check rank and dimension equality '''
        if not len(set([t.rank for t in objects])) == 1:
            raise TypeError("Tensors must have the same rank for merging.")
        if not len(set([t.dim for t in objects])) == 1:
            raise TypeError("Tensors must have the same dimension for merging.")

        ''' merge all objects '''
        remainingObjects = objects[1:] or []
        tensors = objects[0]

        for i, obj in enumerate(remainingObjects):
            tensors = np.append(tensors, obj, axis=0)

        if len(tensors) == 0 and dimension is None:
            for obj in objects:
                kwargs['dim'] = dim(obj)

        return cls.__new__(cls, tensors, **kwargs)

    @classmethod
    def grid(cls, *base_vectors, **kwargs):
        """
        Args:
            baseVector 0 (list/np.array of base coordinates)
            baseVector 1 (list/np.array of base coordinates)
            baseVector 2 (list/np.array of base coordinates)
        Kwargs:
            iter_order (list): order in which the iteration will be done.
                Frequency rises with position in list. default is [0, 1, 2]
                iteration will be done like::
                      
                for v0 in base_vectors[iter_order[0]]:
                    for v1 in base_vectors[iter_order[1]]:
                        for v2 in base_vectors[iter_order[2]]:
                            coords0.append(locals()['v%i' % iter_order[0]])
                            coords1.append(locals()['v%i' % iter_order[1]])
                            coords2.append(locals()['v%i' % iter_order[2]])

        Examples:
            Initilaize using the mgrid notation
            >>> import tfields
            >>> mgrid = tfields.Tensors.grid((0, 1, 2j), (3, 4, 2j), (6, 7, 2j))
            >>> mgrid.equal([[0, 3, 6],
            ...              [0, 3, 7],
            ...              [0, 4, 6],
            ...              [0, 4, 7],
            ...              [1, 3, 6],
            ...              [1, 3, 7],
            ...              [1, 4, 6],
            ...              [1, 4, 7]])
            True
            >>> lins = tfields.Tensors.grid(np.linspace(3, 4, 2), np.linspace(0, 1, 2),
            ...                             np.linspace(6, 7, 2), iter_order=[1, 0, 2])
            >>> lins.equal([[3, 0, 6],
            ...             [3, 0, 7],
            ...             [4, 0, 6],
            ...             [4, 0, 7],
            ...             [3, 1, 6],
            ...             [3, 1, 7],
            ...             [4, 1, 6],
            ...             [4, 1, 7]])
            True
            >>> lins2 = tfields.Tensors.grid(np.linspace(0, 1, 2),
            ...                              np.linspace(3, 4, 2),
            ...                              np.linspace(6, 7, 2),
            ...                              iter_order=[2, 0, 1])
            >>> lins2.equal([[0, 3, 6],
            ...              [0, 4, 6],
            ...              [1, 3, 6],
            ...              [1, 4, 6],
            ...              [0, 3, 7],
            ...              [0, 4, 7],
            ...              [1, 3, 7],
            ...              [1, 4, 7]])
            True

        """
        inst = cls.__new__(cls, tfields.lib.grid.igrid(*base_vectors, **kwargs))
        return inst

    @property
    def rank(self):
        """
        Tensor rank
        """
        return rank(self)

    @property
    def dim(self):
        """
        Manifold dimension
        """
        return dim(self)

    def transform(self, coordSys):
        """
        Args:
            coordSys (str)

        Examples:
            >>> import numpy as np
            >>> import tfields

            CARTESIAN to SPHERICAL
            >>> t = tfields.Tensors([[1, 2, 2], [1, 0, 0], [0, 0, -1], [0, 0, 1], [0, 0, 0]])
            >>> t.transform('spherical')

            r
            >>> assert t[0, 0] == 3

            phi
            >>> assert t[1, 1] == 0.
            >>> assert t[2, 1] == 0.

            theta is 0 at (0, 0, 1) and pi / 2 at (0, 0, -1)
            >>> assert round(t[1, 2], 10) == round(0, 10)
            >>> assert t[2, 2] == -np.pi / 2
            >>> assert t[3, 2] == np.pi / 2

            theta is defined 0 for R == 0
            >>> assert t[4, 0] == 0.
            >>> assert t[4, 2] == 0.


            CARTESIAN to CYLINDER
            >>> tCart = tfields.Tensors([[3, 4, 42], [1, 0, 0], [0, 1, -1], [-1, 0, 1], [0, 0, 0]])
            >>> t_cyl = tCart.copy()
            >>> t_cyl.transform('cylinder')
            >>> assert t_cyl.coordSys == 'cylinder'

            R
            >>> assert t_cyl[0, 0] == 5
            >>> assert t_cyl[1, 0] == 1
            >>> assert t_cyl[2, 0] == 1
            >>> assert t_cyl[4, 0] == 0

            Phi
            >>> assert round(t_cyl[0, 1], 10) == round(np.arctan(4. / 3), 10)
            >>> assert t_cyl[1, 1] == 0
            >>> assert round(t_cyl[2, 1], 10) == round(np.pi / 2, 10)
            >>> assert t_cyl[1, 1] == 0

            Z
            >>> assert t_cyl[0, 2] == 42
            >>> assert t_cyl[2, 2] == -1

            >>> t_cyl.transform('cartesian')
            >>> assert t_cyl.coordSys == 'cartesian'
            >>> assert t_cyl[0, 0] == 3

        """
        #           scalars                 empty             already there
        if self.rank == 0 or self.shape[0] == 0 or self.coordSys == coordSys:
            self.coordSys = coordSys
            return

        tfields.bases.transform(self, self.coordSys, coordSys)
        # self[:] = tfields.bases.transform(self, self.coordSys, coordSys)
        self.coordSys = coordSys

    @contextmanager
    def tmp_transform(self, coordSys):
        """
        Temporarily change the coordSys to another coordSys and change it back at exit
        This method is for cleaner code only.
        No speed improvements go with this.
        Args:
            see transform
        Examples:
            >>> import tfields
            >>> p = tfields.Tensors([[1,2,3]], coordSys=tfields.bases.SPHERICAL)
            >>> with p.tmp_transform(tfields.bases.CYLINDER):
            ...     assert p.coordSys == tfields.bases.CYLINDER
            >>> assert p.coordSys == tfields.bases.SPHERICAL

        """
        baseBefore = self.coordSys
        if baseBefore == coordSys:
            yield
        else:
            self.transform(coordSys)

            yield

            self.transform(baseBefore)

    def mirror(self, coordinate, condition=None):
        """
        Reflect/Mirror the entries meeting <condition> at <coordinate> = 0
        Args:
            coordinate (int): coordinate index
        Examples:
            >>> import tfields
            >>> p = tfields.Tensors([[1., 2., 3.], [4., 5., 6.], [1, 2, -6]])
            >>> p.mirror(1)
            >>> assert p.equal([[1, -2, 3], [4, -5,  6], [1, -2, -6]])

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
690
691
            multiple coordinates can be mirrored at the same time
            i.e. a point mirrorion would be
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
692
693
694
695
696
697
698
699
            >>> p = tfields.Tensors([[1., 2., 3.], [4., 5., 6.], [1, 2, -6]])
            >>> p.mirror([0,2])
            >>> assert p.equal([[-1, 2, -3], [-4, 5, -6], [-1, 2., 6.]])

            You can give a condition as mask or as str.
            The mirroring will only be applied to the points meeting the condition.
            >>> import sympy
            >>> x, y, z = sympy.symbols('x y z')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
700
            >>> p.mirror([0, 2], y > 3)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
701
702
703
704
705
706
707
708
709
710
            >>> p.equal([[-1, 2, -3], [4, 5, 6], [-1, 2, 6]])
            True

        """
        if condition is None:
            condition = np.array([True for i in range(len(self))])
        elif isinstance(condition, sympy.Basic):
            condition = self.evalf(condition)
        if isinstance(coordinate, list) or isinstance(coordinate, tuple):
            for c in coordinate:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
711
                self.mirror(c, condition=condition)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
712
713
714
715
716
717
        elif isinstance(coordinate, int):
            self[:, coordinate][condition] *= -1
        else:
            raise TypeError()

    def to_segment(self, segment, num_segments, coordinate,
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
718
                   periodicity=2 * np.pi, offset=0.,
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
719
720
721
722
723
724
                   coordSys=None):
        """
        For circular (close into themself after
        <periodicity>) coordinates at index <coordinate> assume
        <num_segments> segments and transform all values to
        segment number <segment>
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
725
726
727
728
729
730
731
732
        Args:
            segment (int): segment index (starting at 0)
            num_segments (int): number of segments
            coordinate (int): coordinate index
            periodicity (float): after what lenght, the coordiante repeats
            offset (float): offset in the mapping
            coordSys (str or sympy.CoordinateSystem): in which coord sys the
                transformation should be done
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
        Examples:
            >>> import tfields
            >>> import numpy as np
            >>> pStart = tfields.Points3D([[6, 2 * np.pi, 1],
            ...                            [6, 2 * np.pi / 5 * 3, 1]],
            ...                           coordSys='cylinder')
            >>> p = tfields.Points3D(pStart)
            >>> p.to_segment(0, 5, 1, offset=-2 * np.pi / 10)
            >>> assert np.array_equal(p[:, 1], [0, 0])

            >>> p2 = tfields.Points3D(pStart)
            >>> p2.to_segment(1, 5, 1, offset=-2 * np.pi / 10)
            >>> assert np.array_equal(np.round(p2[:, 1], 4), [1.2566] * 2)

        """
        if segment > num_segments - 1:
            raise ValueError("Segment {0} not existent.".format(segment))

        if coordSys is None:
            coordSys = self.coordSys
        with self.tmp_transform(coordSys):
            # map all values to first segment
            self[:, coordinate] = \
                (self[:, coordinate] - offset) % (periodicity / num_segments) + \
                offset + segment * periodicity / num_segments

    def equal(self, other,
              rtol=None, atol=None, equal_nan=False,
              return_bool=True):
        """
        Evaluate, whether the instance has the same content as other.
        Args:
            optional:
                rtol (float)
                atol (float)
                equal_nan (bool)
            see numpy.isclose
        """
        if issubclass(type(other), Tensors) and self.coordSys != other.coordSys:
            other = other.copy()
            other.transform(self.coordSys)
        x, y = np.asarray(self), np.asarray(other)
        if rtol is None and atol is None:
            mask = (x == y)
            if equal_nan:
                both_nan = np.isnan(x) & np.isnan(y)
                mask[both_nan] = both_nan[both_nan]
        else:
            if rtol is None:
                rtol = 0.
            if atol is None:
                atol = 0.
            mask = np.isclose(x, y, rtol=rtol, atol=atol, equal_nan=equal_nan)
        if return_bool:
            return bool(np.all(mask))
        return mask

    def contains(self, other, **kwargs):
        """
        Inspired by a speed argument @
        stackoverflow.com/questions/14766194/testing-whether-a-numpy-array-contains-a-given-row
        Examples:
            >>> import tfields
            >>> p = tfields.Tensors([[1,2,3], [4,5,6], [6,7,8]])
            >>> p.contains([4,5,6])
            True

        """
        return any(self.equal(other, return_bool=False).all(1))

    def indices(self, tensor):
        """
        Returns:
            list of int: indices of tensor occuring
        """
        indices = []
        for i, p in enumerate(self):
            if all(p == tensor):
                indices.append(i)
        return indices

    def index(self, tensor):
        """
        Args:
            tensor
        Returns:
            int: index of tensor occuring
        """
        indices = self.indices(tensor)
        if not indices:
            return None
        if len(indices) == 1:
            return indices[0]
        raise ValueError("Multiple occurences of value {}"
                         .format(tensor))

    def moments(self, moment):
        """
        Returns:
            Moments of the distribution.
        Note:
            The first moment is given as the mean,
            second as variance etc. Not 0 as it is mathematicaly correct.
        Args:
            moment (int): n-th moment
        """
        return tfields.lib.stats.moments(self, moment)

    def closest(self, other, **kwargs):
        """
        Args:
            other (Tensors): closest points to what? -> other
            **kwargs: forwarded to scipy.spatial.cKDTree.query
        Returns:
            array shape(len(self)): Indices of other points that are closest to own points
        Examples:
            >>> import tfields
            >>> m = tfields.Tensors([[1,0,0], [0,1,0], [1,1,0], [0,0,1],
            ...                      [1,0,1]])
            >>> p = tfields.Tensors([[1.1,1,0], [0,0.1,1], [1,0,1.1]])
            >>> p.closest(m)
            array([2, 3, 4])

        """
        with other.tmp_transform(self.coordSys):
            # balanced_tree option gives huge speedup!
            kd_tree = sp.spatial.cKDTree(other, 1000,
                                         balanced_tree=False)
            res = kd_tree.query(self, **kwargs)
            array = res[1]

        return array

    def evalf(self, expression=None, coordSys=None):
        """
        Args:
            expression (sympy logical expression)
            coordSys (str): coordSys to evalfuate the expression in.
        Returns:
            np.ndarray: mask of dtype bool with lenght of number of points in self.
                 This array is True, where expression evalfuates True.
        Examples:
            >>> import tfields
            >>> import numpy
            >>> import sympy
            >>> x, y, z = sympy.symbols('x y z')
            >>> p = tfields.Tensors([[1., 2., 3.], [4., 5., 6.], [1, 2, -6],
            ...                      [-5, -5, -5], [1,0,-1], [0,1,-1]])
            >>> np.array_equal(p.evalf(x > 0),
            ...                [True, True, True, False, True, False])
            True
            >>> np.array_equal(p.evalf(x >= 0),
            ...                [True, True, True, False, True, True])
            True

            And combination
            >>> np.array_equal(p.evalf((x > 0) & (y < 3)),
            ...                [True, False, True, False, True, False])
            True

            Or combination
            >>> np.array_equal(p.evalf((x > 0) | (y > 3)),
            ...                [True, True, True, False, True, False])
            True

        """
        coords = sympy.symbols('x y z')
        with self.tmp_transform(coordSys or self.coordSys):
            mask = tfields.evalf(self, expression, coords=coords)
        return mask

    def cut(self, expression, coordSys=None):
        """
        Default cut method for Points3D. Works on a copy.
        Args:
            expression (sympy logical expression): logical expression which will be evalfuated.
                             use symbols x, y and z
            coordSys (str): coordSys to evalfuate the expression in.
        Examples:
            >>> import tfields
            >>> import sympy
            >>> x, y, z = sympy.symbols('x y z')
            >>> p = tfields.Tensors([[1., 2., 3.], [4., 5., 6.], [1, 2, -6],
            ...                      [-5, -5, -5], [1,0,-1], [0,1,-1]])
            >>> p.cut(x > 0).equal([[1, 2, 3],
            ...                     [4, 5, 6],
            ...                     [1, 2, -6],
            ...                     [1, 0, -1]])
            True

            combinations of cuts
            >>> p.cut((x > 0) & (z < 0)).equal([[1, 2, -6], [1, 0, -1]])
            True

        Returns:
            copy of self with cut applied

        """
        if len(self) == 0:
            return self.copy()
        mask = self.evalf(expression, coordSys=coordSys or self.coordSys)
        mask.astype(bool)
        inst = self[mask].copy()
        return inst

    def distances(self, other, **kwargs):
        """
        Args:
            other(array)
            **kwargs:
                ... is forwarded to sp.spatial.distance.cdist
        Examples:
            >>> import tfields
            >>> p = tfields.Tensors.grid((0, 2, 3j),
            ...                          (0, 2, 3j),
            ...                          (0, 0, 1j))
            >>> p[4,2] = 1
            >>> p.distances(p)[0,0]
            0.0
            >>> p.distances(p)[5,1]
            1.4142135623730951
            >>> p.distances([[0,1,2]])[-1][0] == 3
            True

        """
        if issubclass(type(other), Tensors) and self.coordSys != other.coordSys:
            other = other.copy()
            other.transform(self.coordSys)
        return sp.spatial.distance.cdist(self, other, **kwargs)

    def min_dists(self, other=None, **kwargs):
        """
        Args:
            other(array | None): if None: closest distance to self
            **kwargs:
                memory_saving (bool): for very large array comparisons
                    default False
                ... rest is forwarded to sp.spatial.distance.cdist

        Returns:
            np.array: minimal distances of self to other


        Examples:
            >>> import tfields
            >>> import numpy as np
            >>> p = tfields.Tensors.grid((0, 2, 3),
            ...                          (0, 2, 3),
            ...                          (0, 0, 1))
            >>> p[4,2] = 1
            >>> dMin = p.min_dists()
            >>> expected = [1] * 9
            >>> expected[4] = np.sqrt(2)
            >>> np.array_equal(dMin, expected)
            True

            >>> dMin2 = p.min_dists(memory_saving=True)
            >>> bool((dMin2 == dMin).all())
            True

        """
        memory_saving = kwargs.pop('memory_saving', False)

        if other is None:
            other = self
        else:
            raise NotImplementedError("Should be easy but make shure not to remove diagonal")

For faster browsing, not all history is shown. View entire blame