core.py 100 KB
Newer Older
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1
2
3
4
5
6
7
8
#!/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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
9
10

Notes:
dboe's avatar
dboe committed
11
12
13
    It could be worthwhile concidering `np.li.mixins.NDArrayOperatorsMixin ...
    <https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/...
    ... numpy.lib.mixins.NDArrayOperatorsMixin.html>`_
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
14
"""
dboe's avatar
dboe committed
15
# builtin
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
16
17
18
19
20
21
import warnings
import pathlib
from six import string_types
from contextlib import contextmanager
from collections import Counter

dboe's avatar
dboe committed
22
# 3rd party
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
23
24
25
import numpy as np
import sympy
import scipy as sp
dboe's avatar
dboe committed
26
import sortedcontainers
27
import rna
dboe's avatar
dboe committed
28

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
29
import tfields.bases
dboe's avatar
dboe committed
30
31

np.seterr(all="warn", over="raise")
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
32
33
34
35
36
37


def rank(tensor):
    """
    Tensor rank
    """
dboe's avatar
dboe committed
38
    tensor = np.asarray(tensor)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
39
40
41
42
43
44
45
    return len(tensor.shape) - 1


def dim(tensor):
    """
    Manifold dimension
    """
dboe's avatar
dboe committed
46
    tensor = np.asarray(tensor)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
47
48
49
50
51
    if rank(tensor) == 0:
        return 1
    return tensor.shape[1]


dboe's avatar
dboe committed
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
class AbstractObject(object):
    def save(self, path, *args, **kwargs):
        """
        Saving 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, pathlib.Path)):
            extension = pathlib.Path(path).suffix.lstrip(".")
        else:
            raise ValueError("Wrong path type {0}".format(type(path)))
        path = str(path)

        # 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())
            )

        path = rna.path.resolve(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
        """
        if isinstance(path, (string_types, pathlib.Path)):
            extension = pathlib.Path(path).suffix.lstrip(".")
            path = str(path)
            path = rna.path.resolve(path)
        else:
            extension = kwargs.pop("extension", "npz")

        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:
            Build some dummies:
            >>> import tfields
            >>> from tempfile import NamedTemporaryFile
            >>> out_file = NamedTemporaryFile(suffix='.npz')
            >>> p = tfields.Points3D([[1., 2., 3.], [4., 5., 6.], [1, 2, -6]],
            ...                      name='my_points')
            >>> scalars = tfields.Tensors([0, 1, 2], name=42)
            >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
            >>> maps = [tfields.TensorFields([[0, 1, 2], [0, 1, 2]], [42, 21]),
            ...         tfields.TensorFields([[1], [2]], [-42, -21])]
            >>> m = tfields.TensorMaps(vectors, scalars,
            ...                        maps=maps)

            Simply give the file name to save
            >>> p.save(out_file.name)
            >>> _ = out_file.seek(0)  # this is only necessary in the test
            >>> p1 = tfields.Points3D.load(out_file.name)
            >>> assert p.equal(p1)
            >>> assert p.coord_sys == p1.coord_sys

            The fully nested structure of a TensorMaps object is reconstructed
            >>> out_file_maps = NamedTemporaryFile(suffix='.npz')
            >>> m.save(out_file_maps.name)
            >>> _ = out_file_maps.seek(0)
            >>> m1 = tfields.TensorMaps.load(out_file_maps.name,
            ...                              allow_pickle=True)
            >>> assert m.equal(m1)
dboe's avatar
dboe committed
146
            >>> assert m.maps[3].dtype == m1.maps[3].dtype
dboe's avatar
dboe committed
147
148
149
150
151
152
153

            Names are preserved
            >>> assert p.name == 'my_points'
            >>> m.names
            [42]

        """
dboe's avatar
dboe committed
154
        content_dict = self._as_new_dict()
dboe's avatar
dboe committed
155
156
157
158
159
160
161
162
163
164
165
166
        np.savez(path, **content_dict)

    @classmethod
    def _load_npz(cls, path, **load_kwargs):
        """
        Factory method
        Given a path to a npz file, construct the object
        """
        # TODO: think about allow_pickle, wheter it really should be True or
        # wheter we could avoid pickling (potential security issue)
        load_kwargs.setdefault('allow_pickle', True)
        np_file = np.load(path, **load_kwargs)
dboe's avatar
dboe committed
167
        return cls._from_new_dict(dict(np_file))
dboe's avatar
dboe committed
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

    def _args(self) -> tuple:
        return tuple()

    def _kwargs(self) -> dict:
        return dict()

    _HIERARCHY_SEPARATOR = '::'

    def _as_new_dict(self):
        d = {}

        # type
        d["type"] = type(self).__name__

        # args and kwargs
        for base_attr, iterable in [
                ('args', ((str(i), arg)
                          for i, arg in enumerate(self._args()))),
                ('kwargs', self._kwargs().items())]:
            for attr, value in iterable:
                attr = base_attr + self._HIERARCHY_SEPARATOR + attr
                if hasattr(value, '_as_new_dict'):
                    part_dict = value._as_new_dict()
                    for part_attr, part_value in part_dict.items():
                        d[
                            attr + self._HIERARCHY_SEPARATOR + part_attr
                        ] = part_value
                else:
                    d[attr] = value
        return d

    @classmethod
    def _from_new_dict(cls, d: dict):
        d.pop('type')

        here = {}
        for string in d:  # TOO no sortelist
            value = d[string]

            attr, _, end = string.partition(cls._HIERARCHY_SEPARATOR)
            key, _, end = end.partition(cls._HIERARCHY_SEPARATOR)
            if attr not in here:
                here[attr] = {}
            if key not in here[attr]:
                here[attr][key] = {}
            here[attr][key][end] = value

        """
        Do the recursion
        """
        for attr in here:
            for key in here[attr]:
dboe's avatar
dboe committed
221
                if 'type' in here[attr][key]:
dboe's avatar
dboe committed
222
                    obj_type = here[attr][key].get("type")
dboe's avatar
dboe committed
223
224
                    if isinstance(obj_type, np.ndarray):  # happens on np.load
                        obj_type = obj_type.tolist()
dboe's avatar
dboe committed
225
226
227
228
229
230
                    if isinstance(obj_type, bytes):
                        # asthonishingly, this is not necessary under linux.
                        # Found under nt. ???
                        obj_type = obj_type.decode("UTF-8")
                    obj_type = getattr(tfields, obj_type)
                    attr_value = obj_type._from_new_dict(here[attr][key])
dboe's avatar
dboe committed
231
                else:  # if len(here[attr][key]) == 1:
dboe's avatar
dboe committed
232
                    attr_value = here[attr][key].pop('')
dboe's avatar
dboe committed
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
                here[attr][key] = attr_value

        '''
        Build the generic way
        '''
        args = here.pop('args', tuple())
        args = tuple(args[key] for key in sorted(args))
        kwargs = here.pop('kwargs', {})
        assert len(here) == 0
        obj = cls(*args, **kwargs)
        return obj

    def _as_dict(self):
        """
        Recursively walk trough all __slots__ and describe all elements
        """
        d = {}
        d["bulk"] = self.bulk
        d["bulk_type"] = self.__class__.__name__
        for attr in self._iter_slots():
            value = getattr(self, attr)

            if hasattr(value, '_as_dict'):
                value = value._as_dict()
            elif isinstance(value, (list)):  # is_iterable
                if len(value) == 0:
                    d[attr] = None
                elif hasattr(value[0], '_as_dict'):
                    for i, part in enumerate(value):
                        part_dict = part._as_dict()
                        for part_attr, part_value in part_dict.items():
                            d[
                                "{attr}::{i}::{part_attr}".format(**locals())
                            ] = part_value
                    continue
            d[attr] = value
        return d

    @classmethod
    def _from_dict(cls, **d):
        """
        legacy method - Opposite of old _as_dict method which is removed in
        favour of nested object saving under 'data'
        """
        list_dict = {}
        kwargs = {}
        """
        De-Flatten the first layer of lists
        """
        for key in sorted(list(d)):
            if "::" in key:
                splits = key.split("::")
                attr, _, end = key.partition("::")
                if attr not in list_dict:
                    list_dict[attr] = {}

                index, _, end = end.partition("::")
                if not index.isdigit():
                    raise ValueError("None digit index given")
                index = int(index)
                if index not in list_dict[attr]:
                    list_dict[attr][index] = {}
                list_dict[attr][index][end] = d[key]
            else:
                kwargs[key] = d[key]

        """
        Build the lists (recursively)
        """
        for key in list(list_dict):
            sub_dict = list_dict[key]
            list_dict[key] = []
            for index in sorted(list(sub_dict)):
                bulk_type = sub_dict[index].get("bulk_type")
                # bulk_type = bulk_type.tolist() was necessary before. no clue
                if isinstance(bulk_type, bytes):
                    # asthonishingly, this is not necessary under linux.
                    # Found under nt. ???
                    bulk_type = bulk_type.decode("UTF-8")
                bulk_type = getattr(tfields, bulk_type)
                list_dict[key].append(bulk_type._from_dict(**sub_dict[index]))

        with cls._bypass_setters('fields', demand_existence=False):
            '''
            Build the normal way
            '''
            bulk = kwargs.pop('bulk')
            bulk_type = kwargs.pop('bulk_type')
            obj = cls.__new__(cls, bulk, **kwargs)

            '''
            Set list attributes
            '''
            for attr, list_value in list_dict.items():
                setattr(obj, attr, list_value)
        return obj


class AbstractNdarray(np.ndarray, AbstractObject):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
332
333
334
335
    """
    All tensors and subclasses should derive from AbstractNdarray.
    AbstractNdarray implements all the inheritance specifics for np.ndarray
    Whene inheriting, three attributes are of interest:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
336
337

    Attributes:
338
        __slots__ (List(str)): If you want to add attributes to
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
339
340
341
342
343
            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.
344
        __slot_dtype__ (List(dtypes)): for the conversion of the
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
345
346
            args in __slots__ to numpy arrays. None values mean no
            conversion.
347
348
349
        __slot_setters__ (List(callable)): Because __slots__ and properties are
            mutually exclusive this is a possibility to take care of proper
            attribute handling. None will be passed for 'not set'.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
350
351
352
353

    Args:
        array (array-like): input array
        **kwargs: arguments corresponding to __slots__
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
354

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
355
356
    TODO:
        equality check
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
357

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
358
    """
dboe's avatar
dboe committed
359

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
360
361
    __slots__ = []
    __slot_defaults__ = []
362
    __slot_dtypes__ = []
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
363
364
365
    __slot_setters__ = []

    def __new__(cls, array, **kwargs):  # pragma: no cover
dboe's avatar
dboe committed
366
367
368
        raise NotImplementedError(
            "{clsType} type must implement '__new__'".format(clsType=type(cls))
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
369
370
371
372
373
374
375
376
377
378
379
380

    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):
dboe's avatar
dboe committed
381
        return [att for att in cls.__slots__ if att != "_cache"]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
382
383
384
385
386

    @classmethod
    def _update_slot_kwargs(cls, kwargs):
        """
        set the defaults in kwargs according to __slot_defaults__
387
        and convert the kwargs according to __slot_dtypes__
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
388
        """
389
        slot_defaults = cls.__slot_defaults__ + [None] * (
dboe's avatar
dboe committed
390
391
            len(cls.__slots__) - len(cls.__slot_defaults__)
        )
392
393
        slot_dtypes = cls.__slot_dtypes__ + [None] * (
            len(cls.__slots__) - len(cls.__slot_dtypes__)
dboe's avatar
dboe committed
394
395
        )
        for attr, default, dtype in zip(
396
            cls.__slots__, slot_defaults, slot_dtypes
dboe's avatar
dboe committed
397
398
        ):
            if attr == "_cache":
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
399
400
401
402
403
404
405
                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:
dboe's avatar
dboe committed
406
407
408
                    raise ValueError(
                        str(attr) + str(dtype) + str(kwargs[attr]) + str(err)
                    )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
409
410
411
412
413
414
415
416
417
418
419
420

    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)

dboe's avatar
dboe committed
421
422
423
424
425
426
    def _args(self):
        return (np.array(self),)

    def _kwargs(self):
        return dict((attr, getattr(self, attr)) for attr in self._iter_slots())

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
427
428
    def __reduce__(self):
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
429
430
        important for pickling (see `here <https://stackoverflow.com/questions/26598109/preserve-custom-attributes-when-pickling-subclass-of-numpy-array>`_)

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
431
432
433
434
435
436
        Examples:
            >>> from tempfile import NamedTemporaryFile
            >>> import pickle
            >>> import tfields

            Build a dummy scalar field
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
437

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
438
439
440
            >>> from tfields import Tensors, TensorFields
            >>> scalars = Tensors([0, 1, 2])
            >>> vectors = Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
dboe's avatar
dboe committed
441
442
443
            >>> scalar_field = TensorFields(vectors,
            ...                             scalars,
            ...                             coord_sys='cylinder')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
444
445

            Save it and restore it
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
446

447
            >>> out_file = NamedTemporaryFile(suffix='.pickle')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
448

449
            >>> pickle.dump(scalar_field,
450
451
            ...             out_file)
            >>> _ = out_file.seek(0)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
452

453
            >>> sf = pickle.load(out_file)
454
            >>> sf.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
455
456
457
458
459
460
461
462
463
            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__
dboe's avatar
dboe committed
464
465
466
        new_state = pickled_state[2] + tuple(
            [getattr(self, slot) for slot in self._iter_slots()]
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
467

dboe's avatar
dboe committed
468
469
        # Return a tuple that replaces the parent's __setstate__
        # tuple with our own
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
470
471
472
473
        return (pickled_state[0], pickled_state[1], new_state)

    def __setstate__(self, state):
        """
474
        Counterpart to __reduce__. Important for unpickling.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
475
476
        """
        # Call the parent's __setstate__ with the other tuple elements.
dboe's avatar
dboe committed
477
        super(AbstractNdarray, self).__setstate__(
dboe's avatar
dboe committed
478
            state[0:-len(self._iter_slots())]
dboe's avatar
dboe committed
479
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
480
481

        # set the __slot__ attributes
482
483
484
485
486
        valid_slot_attrs = list(self._iter_slots())
        added_slot_attrs = ['name']  # attributes that have been added later
                                     # have not been pickled with the full
                                     # information and thus need to be
                                     # excluded from the __setstate__
dboe's avatar
dboe committed
487
488
                                     # need to be in the same order as they
                                     # have been added to __slots__
489
490
491
492
        n_old = len(valid_slot_attrs) - len(state[5:])
        if n_old > 0:
            for latest_index in range(n_old):
                new_slot = added_slot_attrs[-latest_index]
dboe's avatar
dboe committed
493
494
495
496
                warnings.warn("Slots with names '{new_slot}' appears to have "
                              "been added after the creation of the reduced "
                              "state. No corresponding state found in "
                              "__setstate__."
497
498
499
500
501
502
503
                              .format(**locals()))
                valid_slot_attrs.pop(valid_slot_attrs.index(new_slot))
                setattr(self, new_slot, None)

        for slot_index, slot in enumerate(valid_slot_attrs):
            state_index = 5 + slot_index
            setattr(self, slot, state[state_index])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
504

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
505
506
507
508
509
510
511
512
    @property
    def bulk(self):
        """
        The pure ndarray version of the actual state
            -> nothing attached
        """
        return np.array(self)

513
514
    @classmethod
    @contextmanager
dboe's avatar
dboe committed
515
516
517
    def _bypass_setters(cls, *slots,
                        empty_means_all=True,
                        demand_existence=False):
518
519
520
        """
        Temporarily remove the setter in __slot_setters__ corresponding to slot
        position in __slot__. You should know what you do, when using this.
521
522
523
524
525

        Args:
            *slots (str): attribute names in __slots__
            empty_means_all (bool): defines behaviour when slots is empty.
                When True: if slots is empty mute all slots in __slots__
dboe's avatar
dboe committed
526
527
            demand_existence (bool): if false do not check the existence of the
                slot in __slots__ - do nothing for that slot. Handle with care!
528
529
530
531
532
533
        """
        if not slots and empty_means_all:
            slots = cls.__slots__
        slot_indices = []
        setters = []
        for slot in slots:
dboe's avatar
dboe committed
534
535
536
537
538
539
540
541
            slot_index = cls.__slots__.index(slot)\
                if slot in cls.__slots__ else None
            if slot_index is None:
                # slot not in cls.__slots__.
                if demand_existence:
                    raise ValueError(
                        "Slot {slot} not existing".format(**locals()))
                continue
542
543
544
545
546
547
548
            if len(cls.__slot_setters__) < slot_index + 1:
                # no setter to be found
                continue
            slot_indices.append(slot_index)
            setter = cls.__slot_setters__[slot_index]
            setters.append(setter)
            cls.__slot_setters__[slot_index] = None
549
        yield
550
551
        for slot_index, setter in zip(slot_indices, setters):
            cls.__slot_setters__[slot_index] = setter
552

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
553
554
555
    def copy(self, *args, **kwargs):
        """
        The standard ndarray copy does not copy slots. Correct for this.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
556

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
557
558
        Examples:
            >>> import tfields
dboe's avatar
dboe committed
559
560
            >>> m = tfields.TensorMaps(
            ...     [[1,2,3], [3,3,3], [0,0,0], [5,6,7]],
561
562
563
564
565
            ...     maps=[
            ...         ([[0, 1, 2], [1, 2, 3]], [21, 42]),
            ...          [[1]],
            ...          [[0, 1, 2, 3]]
            ...     ])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
566
            >>> mc = m.copy()
dboe's avatar
dboe committed
567
568
            >>> mc.equal(m)
            True
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
569
570
            >>> mc is m
            False
dboe's avatar
dboe committed
571
            >>> mc.maps[3].fields[0] is m.maps[3].fields[0]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
572
573
            False

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
574
        TODO:
dboe's avatar
dboe committed
575
576
            This function implementation could be more general or maybe
            redirect to deepcopy?
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
577
        """
dboe's avatar
dboe committed
578
        inst = super().copy(*args, **kwargs)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
579
580
        for attr in self._iter_slots():
            value = getattr(self, attr)
dboe's avatar
dboe committed
581
            if hasattr(value, "copy") and not isinstance(value, list):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
582
583
584
585
                setattr(inst, attr, value.copy(*args, **kwargs))
            elif isinstance(value, list):
                list_copy = []
                for item in value:
dboe's avatar
dboe committed
586
                    if hasattr(item, "copy"):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
587
588
589
590
591
592
593
594
595
596
597
                        list_copy.append(item.copy(*args, **kwargs))
                    else:
                        list_copy.append(item)
                setattr(inst, attr, list_copy)

        return inst


class Tensors(AbstractNdarray):
    """
    Set of tensors with the same basis.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
598

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
599
600
    TODO:
        all slot args should be protected -> _base
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
601

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
602
603
    Args:
        tensors: np.ndarray or AbstractNdarray subclass
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
604
605
        **kwargs:
            name: optional - custom name, can be anything
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
606

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
607
608
    Examples:
        >>> import numpy as np
609
        >>> import tfields
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
610
611

        Initialize a scalar range
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
612

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
613
614
615
616
617
        >>> scalars = tfields.Tensors([0, 1, 2])
        >>> scalars.rank == 0
        True

        Initialize vectors
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
618

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
619
620
621
622
623
        >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
        >>> vectors.rank == 1
        True
        >>> vectors.dim == 3
        True
624
        >>> assert vectors.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
625
626

        Initialize the Levi-Zivita Tensor
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
627

628
629
630
631
        >>> 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]]])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
632
633
634
635
636
637
638
639
        >>> matrices.shape == (3, 3, 3)
        True
        >>> matrices.rank == 2
        True
        >>> matrices.dim == 3
        True

        Initializing in different start coordinate system
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
640

dboe's avatar
dboe committed
641
642
        >>> cyl = tfields.Tensors([[5, np.arctan(4. / 3.), 42]],
        ...                       coord_sys='cylinder')
643
        >>> assert cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
644
        >>> cyl.transform('cartesian')
645
        >>> assert cyl.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
646
647
648
649
650
651
        >>> 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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
652

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
653
654
        >>> with vectors.tmp_transform('cylinder'):
        ...     vect_cyl = tfields.Tensors(vectors)
655
656
        ...     assert vect_cyl.coord_sys == vectors.coord_sys
        >>> assert vect_cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
657
658

        You can demand a special dimension.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
659

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
660
661
662
663
664
665
666
667
        >>> _ = 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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
668

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
669
670
671
672
673
674
675
676
        >>> _ = 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)

    """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
677
    __slots__ = ['coord_sys', 'name']
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
678
679
680
681
    __slot_defaults__ = ['cartesian']
    __slot_setters__ = [tfields.bases.get_coord_system_name]

    def __new__(cls, tensors, **kwargs):
dboe's avatar
dboe committed
682
683
684
        dtype = kwargs.pop("dtype", None)
        order = kwargs.pop("order", None)
        dim = kwargs.pop("dim", None)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
685

dboe's avatar
dboe committed
686
        """ copy constructor extracts the kwargs from tensors"""
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
687
688
689
        if issubclass(type(tensors), Tensors):
            if dim is not None:
                dim = tensors.dim
dboe's avatar
dboe committed
690
            coord_sys = kwargs.pop("coord_sys", tensors.coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
691
            tensors = tensors.copy()
692
693
            tensors.transform(coord_sys)
            kwargs['coord_sys'] = coord_sys
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
694
            kwargs['name'] = kwargs.pop('name', tensors.name)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
695
696
697
698
            if dtype is None:
                dtype = tensors.dtype
        else:
            if dtype is None:
dboe's avatar
dboe committed
699
                if hasattr(tensors, "dtype"):
700
701
702
                    dtype = tensors.dtype
                else:
                    dtype = np.float64
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
703

dboe's avatar
dboe committed
704
        """ demand iterable structure """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
705
706
707
        try:
            len(tensors)
        except TypeError as err:
dboe's avatar
dboe committed
708
709
710
711
            raise TypeError(
                "Iterable structure necessary."
                " Got {tensors}".format(**locals())
            )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
712

dboe's avatar
dboe committed
713
        """ process empty inputs """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
714
715
716
717
718
719
720
721
        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
dboe's avatar
dboe committed
722
723
            elif hasattr(tensors, 'shape'):
                dim = dim(tensors)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
724
            else:
dboe's avatar
dboe committed
725
                raise ValueError(
dboe's avatar
dboe committed
726
                    "Empty tensors need dimension parameter 'dim'."
dboe's avatar
dboe committed
727
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
728
729
730
731

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

dboe's avatar
dboe committed
732
        """ check dimension(s) """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
733
734
        for d in obj.shape[1:]:
            if not d == obj.dim:
dboe's avatar
dboe committed
735
736
737
738
739
740
741
                raise ValueError(
                    "Dimensions are inconstistent. "
                    "Manifold dimension is {obj.dim}. "
                    "Found dimensions {found} in {obj}.".format(
                        found=obj.shape[1:], **locals()
                    )
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
742
743
        if dim is not None:
            if dim != obj.dim:
dboe's avatar
dboe committed
744
745
746
747
                raise ValueError(
                    "Incorrect dimension: {obj.dim} given,"
                    " {dim} demanded.".format(**locals())
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
748

dboe's avatar
dboe committed
749
        """ update kwargs with defaults from slots """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
750
751
        cls._update_slot_kwargs(kwargs)

dboe's avatar
dboe committed
752
        """ set kwargs to slots attributes """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
753
754
        for attr in kwargs:
            if attr not in cls._iter_slots():
dboe's avatar
dboe committed
755
756
757
758
                raise AttributeError(
                    "Keyword argument {attr} not accepted "
                    "for class {cls}".format(**locals())
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
759
760
761
762
            setattr(obj, attr, kwargs[attr])

        return obj

763
764
765
766
    def __iter__(self):
        """
        Forwarding iterations to the bulk array. Otherwise __getitem__ would
        kick in and slow down imensely.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
767

768
769
770
        Examples:
            >>> import tfields
            >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
dboe's avatar
dboe committed
771
772
            >>> scalar_field = tfields.TensorFields(
            ...     vectors, [42, 21, 10.5], [1, 2, 3])
773
774
775
776
777
778
779
            >>> [(point.rank, point.dim) for point in scalar_field]
            [(0, 1), (0, 1), (0, 1)]

        """
        for index in range(len(self)):
            yield super(Tensors, self).__getitem__(index).view(Tensors)

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
780
781
782
783
    @classmethod
    def merged(cls, *objects, **kwargs):
        """
        Factory method
dboe's avatar
dboe committed
784
        Merges all input arguments to one object
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
785

786
787
788
        Args:
            return_templates (bool): return the templates which can be used
                together with cut to retrieve the original objects
dboe's avatar
dboe committed
789
790
            dim (int):
            **kwargs: passed to cls
791

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
792
793
794
795
796
        Examples:
            >>> import numpy as np
            >>> import tfields
            >>> import tfields.bases

797
798
            The new object with turn out in the most frequent coordinate
            system if not specified explicitly
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
799

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
800
            >>> vec_a = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
dboe's avatar
dboe committed
801
802
803
804
805
806
            >>> vec_b = tfields.Tensors([[5, 4, 1]],
            ...     coord_sys=tfields.bases.cylinder)
            >>> vec_c = tfields.Tensors([[4, 2, 3]],
            ...     coord_sys=tfields.bases.cylinder)
            >>> merge = tfields.Tensors.merged(
            ...     vec_a, vec_b, vec_c, [[2, 0, 1]])
807
            >>> assert merge.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
808
809
810
811
812
813
814
815
            >>> 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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
816

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
817
818
            >>> tm_a = tfields.TensorMaps(merge, maps=[[[0, 1, 2]]])
            >>> tm_b = tm_a.copy()
819
            >>> assert tm_a.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
820
            >>> tm_merge = tfields.TensorMaps.merged(tm_a, tm_b)
821
            >>> assert tm_merge.coord_sys == 'cylinder'
dboe's avatar
dboe committed
822
            >>> assert tm_merge.maps[3].equal([[0, 1, 2],
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
823
824
825
            ...                               list(range(len(merge),
            ...                                          len(merge) + 3,
            ...                                          1))])
dboe's avatar
dboe committed
826

827
828
            >>> obj_list = [tfields.Tensors([[1, 2, 3]],
            ...             coord_sys=tfields.bases.CYLINDER),
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
829
830
            ...             tfields.Tensors([[3] * 3]),
            ...             tfields.Tensors([[5, 1, 3]])]
831
832
            >>> merge2 = tfields.Tensors.merged(
            ...     *obj_list, coord_sys=tfields.bases.CARTESIAN)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
833
834
            >>> assert merge2.equal([[-0.41614684, 0.90929743, 3.],
            ...                      [3, 3, 3], [5, 1, 3]], atol=1e-8)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
835

836
837
838
839
840
841
842
843
844
            The return_templates argument allows to retrieve a template which
            can be used with the cut method.

            >>> merge, templates = tfields.Tensors.merged(
            ...     vec_a, vec_b, vec_c, return_templates=True)
            >>> assert merge.cut(templates[0]).equal(vec_a)
            >>> assert merge.cut(templates[1]).equal(vec_b)
            >>> assert merge.cut(templates[2]).equal(vec_c)

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
845
846
        """

dboe's avatar
dboe committed
847
848
        """ get most frequent coord_sys or predefined coord_sys """
        coord_sys = kwargs.get("coord_sys", None)
849
        return_templates = kwargs.pop("return_templates", False)
850
        if coord_sys is None:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
851
852
853
            bases = []
            for t in objects:
                try:
854
                    bases.append(t.coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
855
856
857
                except AttributeError:
                    pass
            if bases:
858
                # get most frequent coord_sys
dboe's avatar
dboe committed
859
860
861
                coord_sys = sorted(
                    bases, key=Counter(bases).get, reverse=True
                )[0]
dboe's avatar
dboe committed
862
                kwargs["coord_sys"] = coord_sys
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
863
            else:
dboe's avatar
dboe committed
864
865
866
867
                default = cls.__slot_defaults__[
                    cls.__slots__.index("coord_sys")
                ]
                kwargs["coord_sys"] = default
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
868

dboe's avatar
dboe committed
869
        """ transform all raw inputs to cls type with correct coord_sys. Also
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
870
        automatically make a copy of those instances that are of the correct
dboe's avatar
dboe committed
871
        type already."""
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
872
        objects = [cls.__new__(cls, t, **kwargs) for t in objects]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
873

dboe's avatar
dboe committed
874
        """ check rank and dimension equality """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
875
876
877
878
879
        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.")

dboe's avatar
dboe committed
880
        """ merge all objects """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
881
882
883
884
885
886
        remainingObjects = objects[1:] or []
        tensors = objects[0]

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

dboe's avatar
dboe committed
887
        if len(tensors) == 0 and not kwargs.get('dim', None):
888
889
            # if you can not determine the tensor dimension, search for the
            # first object with some entries
dboe's avatar
dboe committed
890
            kwargs['dim'] = dim(objects[0])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
891

892
893
894
895
896
897
898
899
900
901
902
903
        if not return_templates:
            return cls.__new__(cls, tensors, **kwargs)
        else:
            tensor_lengths = [len(o) for o in objects]
            cum_tensor_lengths = [sum(tensor_lengths[:i])
                                  for i in range(len(objects))]
            templates = [
                tfields.TensorFields(
                    obj,
                    np.arange(tensor_lengths[i]) + cum_tensor_lengths[i])
                for i, obj in enumerate(objects)]
            return cls.__new__(cls, tensors, **kwargs), templates
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
904
905
906
907
908

    @classmethod
    def grid(cls, *base_vectors, **kwargs):
        """
        Args:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
909
910
911
912
913
914
915
            *base_vectors (Iterable): base coordinates. The amount of base
                vectors defines the dimension

            **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::
dboe's avatar
dboe committed
916

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
917
918
919
920
921
922
                    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]])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
923
924
925

        Examples:
            Initilaize using the mgrid notation
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
926

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
927
928
929
930
931
932
933
934
935
936
937
            >>> 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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
938
939
940

            Lists or arrays are accepted also.
            Furthermore, the iteration order can be changed
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
941

dboe's avatar
dboe committed
942
943
944
            >>> lins = tfields.Tensors.grid(
            ...     np.linspace(3, 4, 2), np.linspace(0, 1, 2),
            ...     np.linspace(6, 7, 2), iter_order=[1, 0, 2])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
            >>> 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

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
968
969
            When given the coord_sys argument, the grid is performed in the
            given coorinate system:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
970

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
971
972
973
974
975
976
977
978
979
            >>> lins3 = tfields.Tensors.grid(np.linspace(4, 9, 2),
            ...                              np.linspace(np.pi/2, np.pi/2, 1),
            ...                              np.linspace(4, 4, 1),
            ...                              iter_order=[2, 0, 1],
            ...                              coord_sys=tfields.bases.CYLINDER)
            >>> assert lins3.coord_sys == 'cylinder'
            >>> lins3.transform('cartesian')
            >>> assert np.array_equal(lins3[:, 1], [4, 9])

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
980
        """
dboe's avatar
dboe committed
981
982
983
984
985
986
987
988
        cls_kwargs = {
            attr: kwargs.pop(attr)
            for attr in list(kwargs)
            if attr in cls.__slots__
        }
        inst = cls.__new__(
            cls, tfields.lib.grid.igrid(*base_vectors, **kwargs), **cls_kwargs
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
        return inst

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

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

1005
    def transform(self, coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1006
1007
        """
        Args:
1008
            coord_sys (str)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1009
1010
1011
1012
1013
1014

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

            CARTESIAN to SPHERICAL
dboe's avatar
dboe committed
1015
1016
            >>> t = tfields.Tensors([[1, 2, 2], [1, 0, 0], [0, 0, -1],
            ...                      [0, 0, 1], [0, 0, 0]])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1017
1018
1019
            >>> t.transform('spherical')

            r
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1020

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1021
1022
1023
            >>> assert t[0, 0] == 3

            phi
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1024

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1025
1026
1027
1028
            >>> assert t[1, 1] == 0.
            >>> assert t[2, 1] == 0.

            theta is 0 at (0, 0, 1) and pi / 2 at (0, 0, -1)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1029

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1030
1031
1032
1033
1034
            >>> 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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1035

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1036
1037
1038
1039
1040
            >>> assert t[4, 0] == 0.
            >>> assert t[4, 2] == 0.


            CARTESIAN to CYLINDER
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1041

dboe's avatar
dboe committed
1042
1043
            >>> tCart = tfields.Tensors([[3, 4, 42], [1, 0, 0], [0, 1, -1],
            ...                          [-1, 0, 1], [0, 0, 0]])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1044
1045
            >>> t_cyl = tCart.copy()
            >>> t_cyl.transform('cylinder')
1046
            >>> assert t_cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1047
1048

            R
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1049

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1050
1051
1052
1053
1054
1055
            >>> 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
dboe's avatar
dboe committed
1056

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1057
1058
1059
1060
1061
1062
            >>> 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
dboe's avatar
dboe committed
1063

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1064
1065
1066
1067
            >>> assert t_cyl[0, 2] == 42
            >>> assert t_cyl[2, 2] == -1

            >>> t_cyl.transform('cartesian')
1068
            >>> assert t_cyl.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1069
1070
1071
1072
            >>> assert t_cyl[0, 0] == 3

        """
        #           scalars                 empty             already there
1073
1074
        if self.rank == 0 or self.shape[0] == 0 or self.coord_sys == coord_sys:
            self.coord_sys = coord_sys
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1075
1076
            return

1077
1078
1079
        tfields.bases.transform(self, self.coord_sys, coord_sys)
        # self[:] = tfields.bases.transform(self, self.coord_sys, coord_sys)
        self.coord_sys = coord_sys
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1080
1081

    @contextmanager
1082
    def tmp_transform(self, coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1083
        """
1084
        Temporarily change the coord_sys to another coord_sys and change it back at exit
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1085
1086
        This method is for cleaner code only.
        No speed improvements go with this.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1087

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1088
1089
        Args:
            see transform
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1090

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1091
1092
        Examples:
            >>> import tfields
1093
            >>> p = tfields.Tensors([[1,2,3]], coord_sys=tfields.bases.SPHERICAL)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1094
            >>> with p.tmp_transform(tfields.bases.CYLINDER):
1095
1096
            ...     assert p.coord_sys == tfields.bases.CYLINDER
            >>> assert p.coord_sys == tfields.bases.SPHERICAL
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1097
1098

        """
1099
1100
        baseBefore = self.coord_sys
        if baseBefore == coord_sys:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1101
1102
            yield
        else:
1103
            self.transform(coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1104
1105
1106
1107
1108
1109
1110
1111

            yield

            self.transform(baseBefore)

    def mirror(self, coordinate, condition=None):
        """
        Reflect/Mirror the entries meeting <condition> at <coordinate> = 0
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1112

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1113
1114
        Args:
            coordinate (int): coordinate index
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1115

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1116
1117
1118
1119
1120
1121
        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
1122
1123
            multiple coordinates can be mirrored at the same time
            i.e. a point mirrorion would be
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1124

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1125
1126
1127
1128
1129
            >>> 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.
dboe's avatar
dboe committed
1130
1131
            The mirroring will only be applied to the points meeting the
            condition.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1132

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1133
1134
            >>> import sympy
            >>> x, y, z = sympy.symbols('x y z')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1135
            >>> p.mirror([0, 2], y > 3)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
            >>> 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
1146
                self.mirror(c, condition=condition)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1147
1148
1149
1150
1151
        elif isinstance(coordinate, int):
            self[:, coordinate][condition] *= -1
        else:
            raise TypeError()

dboe's avatar
dboe committed
1152
1153
1154
1155
1156
1157
1158
1159
1160
    def to_segment(
        self,
        segment,
        num_segments,
        coordinate,
        periodicity=2 * np.pi,
        offset=0.0,
        coord_sys=None,
    ):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1161
1162
1163
1164
1165
        """
        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
1166

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1167
1168
1169
1170
1171
1172
        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
1173
            coord_sys (str or sympy.CoordinateSystem): in which coord sys the
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1174
                transformation should be done
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1175

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1176
1177
1178
1179
1180
        Examples:
            >>> import tfields
            >>> import numpy as np
            >>> pStart = tfields.Points3D([[6, 2 * np.pi, 1],
            ...                            [6, 2 * np.pi / 5 * 3, 1]],
1181
            ...                           coord_sys='cylinder')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
            >>> 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))

1194
1195
1196
        if coord_sys is None:
            coord_sys = self.coord_sys
        with self.tmp_transform(coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1197
            # map all values to first segment
dboe's avatar
dboe committed
1198
1199
1200
1201
1202
            self[:, coordinate] = (
                (self[:, coordinate] - offset) % (periodicity / num_segments)
                + offset
                + segment * periodicity / num_segments
            )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1203

dboe's avatar
dboe committed
1204
1205
1206
    def equal(
        self, other, rtol=None, atol=None, equal_nan=False, return_bool=True
    ):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1207
1208
        """
        Evaluate, whether the instance has the same content as other.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1209

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1210
1211
1212
1213
1214
1215
1216
        Args:
            optional:
                rtol (float)
                atol (float)
                equal_nan (bool)
            see numpy.isclose
        """
dboe's avatar
dboe committed
1217
1218
1219
1220
        if (
            issubclass(type(other), Tensors)
            and self.coord_sys != other.coord_sys
        ):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1221
            other = other.copy()
1222
            other.transform(self.coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1223
1224
        x, y = np.asarray(self), np.asarray(other)
        if rtol is None and atol is None:
dboe's avatar
dboe committed
1225
            mask = x == y
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1226
1227
1228
1229
1230
            if equal_nan:
                both_nan = np.isnan(x) & np.isnan(y)
                mask[both_nan] = both_nan[both_nan]
        else:
            if rtol is None:
dboe's avatar
dboe committed
1231
                rtol = 0.0
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1232
            if atol is None:
dboe's avatar
dboe committed
1233
                atol = 0.0
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1234
1235
1236
1237
1238
1239
1240
1241
1242
            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
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1243

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1244
1245
1246
1247
1248
1249
1250
1251
1252
        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))

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1253
    def indices(self, tensor, rtol=None, atol=None):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1254
1255
1256
        """
        Returns:
            list of int: indices of tensor occuring
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1257

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1258
        Examples:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1259
            Rank 1 Tensors
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1260

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1261
1262
1263
1264
1265
1266
1267
1268
            >>> import tfields
            >>> p = tfields.Tensors([[1,2,3], [4,5,6], [6,7,8], [4,5,6],
            ...                      [4.1, 5, 6]])
            >>> p.indices([4,5,6])
            array([1, 3])
            >>> p.indices([4,5,6.1], rtol=1e-5, atol=1e-1)
            array([1, 3, 4])

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1269
            Rank 0 Tensors
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1270

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1271
1272
1273
1274
1275
1276
            >>> p = tfields.Tensors([2, 3, 6, 3.01])
            >>> p.indices(3)
            array([1])
            >>> p.indices(3, rtol=1e-5, atol=1e-1)
            array([1, 3])

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1277
        """
1278
1279
        x, y = np.asarray(self), np.asarray(tensor)
        if rtol is None and atol is None:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1280
            equal_method = np.equal
1281
1282
        else:
            equal_method = lambda a, b: np.isclose(a, b, rtol=rtol, atol=atol)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1283
1284

        # inspired by https://stackoverflow.com/questions/19228295/find-ordered-vector-in-numpy-array
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1285
        if self.rank == 0:
dboe's avatar
dboe committed
1286
            indices = np.where(equal_method((x - y), 0))[0]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1287
        elif self.rank == 1:
dboe's avatar
dboe committed
1288
            indices = np.where(np.all(equal_method((x - y), 0), axis=1))[0]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1289
1290
        else:
            raise NotImplementedError()
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1291
1292
        return indices

1293
    def index(self, tensor, **kwargs):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1294
1295
1296
        """
        Args:
            tensor
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1297

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1298
1299
1300
        Returns:
            int: index of tensor occuring
        """
1301
        indices = self.indices(tensor, **kwargs)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1302
1303
1304
1305
        if not indices:
            return None
        if len(indices) == 1:
            return indices[0]
dboe's avatar
dboe committed
1306
        raise ValueError("Multiple occurences of value {}".format(tensor))
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1307

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1308