core.py 96.4 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
import warnings
import pathlib
from six import string_types
from contextlib import contextmanager
from collections import Counter
dboe's avatar
dboe committed
21
from copy import deepcopy
dboe's avatar
dboe committed
22
import logging
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
23

dboe's avatar
dboe committed
24
# 3rd party
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
25
26
27
import numpy as np
import sympy
import scipy as sp
dboe's avatar
dboe committed
28
import sortedcontainers
29
import rna
dboe's avatar
dboe committed
30

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
31
import tfields.bases
dboe's avatar
dboe committed
32
33

np.seterr(all="warn", over="raise")
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
34
35
36
37
38
39


def rank(tensor):
    """
    Tensor rank
    """
dboe's avatar
dboe committed
40
    tensor = np.asarray(tensor)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
41
42
43
44
45
46
47
    return len(tensor.shape) - 1


def dim(tensor):
    """
    Manifold dimension
    """
dboe's avatar
dboe committed
48
    tensor = np.asarray(tensor)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
49
50
51
52
53
    if rank(tensor) == 0:
        return 1
    return tensor.shape[1]


dboe's avatar
dboe committed
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
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()))
dboe's avatar
dboe committed
77
        except AttributeError:
dboe's avatar
dboe committed
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
            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))
dboe's avatar
dboe committed
108
        except AttributeError:
dboe's avatar
dboe committed
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
            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
148
            >>> assert m.maps[3].dtype == m1.maps[3].dtype
dboe's avatar
dboe committed
149
150
151
152
153
154
155

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

        """
dboe's avatar
dboe committed
156
        content_dict = self._as_dict()
157
        content_dict["tfields_version"] = tfields.__version__
dboe's avatar
dboe committed
158
159
160
161
162
163
164
165
166
167
        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)
168
        load_kwargs.setdefault("allow_pickle", True)
dboe's avatar
dboe committed
169
        np_file = np.load(path, **load_kwargs)
dboe's avatar
dboe committed
170
        d = dict(np_file)
171
        d.pop("tfields_version", None)
dboe's avatar
dboe committed
172
        return cls._from_dict(d)
dboe's avatar
dboe committed
173
174
175
176
177
178
179

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

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

180
    _HIERARCHY_SEPARATOR = "::"
dboe's avatar
dboe committed
181

dboe's avatar
dboe committed
182
    def _as_dict(self):
dboe's avatar
dboe committed
183
184
185
186
187
188
189
        d = {}

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

        # args and kwargs
        for base_attr, iterable in [
190
191
192
            ("args", ((str(i), arg) for i, arg in enumerate(self._args()))),
            ("kwargs", self._kwargs().items()),
        ]:
dboe's avatar
dboe committed
193
194
            for attr, value in iterable:
                attr = base_attr + self._HIERARCHY_SEPARATOR + attr
195
                if hasattr(value, "_as_dict"):
dboe's avatar
dboe committed
196
                    part_dict = value._as_dict()
dboe's avatar
dboe committed
197
                    for part_attr, part_value in part_dict.items():
198
                        d[attr + self._HIERARCHY_SEPARATOR + part_attr] = part_value
dboe's avatar
dboe committed
199
200
201
202
203
                else:
                    d[attr] = value
        return d

    @classmethod
dboe's avatar
dboe committed
204
205
    def _from_dict(cls, d: dict):
        try:
206
            d.pop("type")
dboe's avatar
dboe committed
207
208
209
        except KeyError:
            # legacy
            return cls._from_dict_legacy(**d)
dboe's avatar
dboe committed
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227

        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]:
228
                if "type" in here[attr][key]:
dboe's avatar
dboe committed
229
                    obj_type = here[attr][key].get("type")
dboe's avatar
dboe committed
230
231
                    if isinstance(obj_type, np.ndarray):  # happens on np.load
                        obj_type = obj_type.tolist()
dboe's avatar
dboe committed
232
233
234
235
236
                    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)
dboe's avatar
dboe committed
237
                    attr_value = obj_type._from_dict(here[attr][key])
dboe's avatar
dboe committed
238
                else:  # if len(here[attr][key]) == 1:
239
                    attr_value = here[attr][key].pop("")
dboe's avatar
dboe committed
240
241
                here[attr][key] = attr_value

242
        """
dboe's avatar
dboe committed
243
        Build the generic way
244
245
        """
        args = here.pop("args", tuple())
dboe's avatar
dboe committed
246
        args = tuple(args[key] for key in sorted(args))
247
        kwargs = here.pop("kwargs", {})
dboe's avatar
dboe committed
248
249
250
251
252
        assert len(here) == 0
        obj = cls(*args, **kwargs)
        return obj

    @classmethod
dboe's avatar
dboe committed
253
    def _from_dict_legacy(cls, **d):
dboe's avatar
dboe committed
254
        """
dboe's avatar
dboe committed
255
256
        legacy method of _from_dict - Opposite of old _as_dict method
        which is overridden in this version
dboe's avatar
dboe committed
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
        """
        list_dict = {}
        kwargs = {}
        """
        De-Flatten the first layer of lists
        """
        for key in sorted(list(d)):
            if "::" in key:
                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")
dboe's avatar
dboe committed
287
                bulk_type = bulk_type.tolist()
dboe's avatar
dboe committed
288
289
290
291
292
                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)
dboe's avatar
dboe committed
293
                list_dict[key].append(bulk_type._from_dict_legacy(**sub_dict[index]))
dboe's avatar
dboe committed
294

295
296
        with cls._bypass_setters("fields", demand_existence=False):
            """
dboe's avatar
dboe committed
297
            Build the normal way
298
299
300
            """
            bulk = kwargs.pop("bulk")
            bulk_type = kwargs.pop("bulk_type")
dboe's avatar
dboe committed
301
302
            obj = cls.__new__(cls, bulk, **kwargs)

303
            """
dboe's avatar
dboe committed
304
            Set list attributes
305
            """
dboe's avatar
dboe committed
306
307
308
309
310
311
            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
312
313
314
315
    """
    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
316
317

    Attributes:
318
        __slots__ (List(str)): If you want to add attributes to
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
319
320
321
322
323
            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.
324
        __slot_dtype__ (List(dtypes)): for the conversion of the
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
325
326
            args in __slots__ to numpy arrays. None values mean no
            conversion.
327
328
329
        __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
330
331
332
333

    Args:
        array (array-like): input array
        **kwargs: arguments corresponding to __slots__
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
334

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
335
336
    TODO:
        equality check
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
337

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
338
    """
dboe's avatar
dboe committed
339

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
340
341
    __slots__ = []
    __slot_defaults__ = []
342
    __slot_dtypes__ = []
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
343
344
345
    __slot_setters__ = []

    def __new__(cls, array, **kwargs):  # pragma: no cover
dboe's avatar
dboe committed
346
347
348
        raise NotImplementedError(
            "{clsType} type must implement '__new__'".format(clsType=type(cls))
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
349
350
351
352
353
354
355
356
357
358
359
360

    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
361
        return [att for att in cls.__slots__ if att != "_cache"]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
362
363
364
365
366

    @classmethod
    def _update_slot_kwargs(cls, kwargs):
        """
        set the defaults in kwargs according to __slot_defaults__
367
        and convert the kwargs according to __slot_dtypes__
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
368
        """
369
        slot_defaults = cls.__slot_defaults__ + [None] * (
dboe's avatar
dboe committed
370
371
            len(cls.__slots__) - len(cls.__slot_defaults__)
        )
372
373
        slot_dtypes = cls.__slot_dtypes__ + [None] * (
            len(cls.__slots__) - len(cls.__slot_dtypes__)
dboe's avatar
dboe committed
374
        )
375
        for attr, default, dtype in zip(cls.__slots__, slot_defaults, slot_dtypes):
dboe's avatar
dboe committed
376
            if attr == "_cache":
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
377
378
379
380
381
382
383
                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
384
385
386
                    raise ValueError(
                        str(attr) + str(dtype) + str(kwargs[attr]) + str(err)
                    )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
387
388
389
390
391
392
393
394

    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
395
396
            if isinstance(setter, str):
                setter = getattr(self, setter)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
397
398
399
400
            if setter is not None:
                value = setter(value)
        super(AbstractNdarray, self).__setattr__(name, value)

dboe's avatar
dboe committed
401
402
403
404
405
406
    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
407
408
    def __reduce__(self):
        """
dboe's avatar
dboe committed
409
410
        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
411

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
412
413
414
415
416
417
        Examples:
            >>> from tempfile import NamedTemporaryFile
            >>> import pickle
            >>> import tfields

            Build a dummy scalar field
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
418

dboe's avatar
dboe committed
419
420
421
422
423
424
            >>> scalars = tfields.Tensors([0, 1, 2])
            >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
            >>> scalar_field = tfields.TensorFields(
            ...     vectors,
            ...     scalars,
            ...     coord_sys='cylinder')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
425
426

            Save it and restore it
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
427

428
            >>> out_file = NamedTemporaryFile(suffix='.pickle')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
429

430
            >>> pickle.dump(scalar_field,
431
432
            ...             out_file)
            >>> _ = out_file.seek(0)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
433

434
            >>> sf = pickle.load(out_file)
435
            >>> sf.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
436
437
438
439
440
441
442
443
444
            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
445
446
447
        new_state = pickled_state[2] + tuple(
            [getattr(self, slot) for slot in self._iter_slots()]
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
448

dboe's avatar
dboe committed
449
450
        # Return a tuple that replaces the parent's __setstate__
        # tuple with our own
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
451
452
453
454
        return (pickled_state[0], pickled_state[1], new_state)

    def __setstate__(self, state):
        """
455
        Counterpart to __reduce__. Important for unpickling.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
456
457
        """
        # Call the parent's __setstate__ with the other tuple elements.
dboe's avatar
dboe committed
458
        super(AbstractNdarray, self).__setstate__(
459
            state[0: -len(self._iter_slots())]
dboe's avatar
dboe committed
460
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
461
462

        # set the __slot__ attributes
463
        valid_slot_attrs = list(self._iter_slots())
dboe's avatar
dboe committed
464
465
466
467
468
        """
        attributes that have been added later have not been pickled with the
        full information and thus need to be excluded from the __setstate__
        need to be in the same order as they have been added to __slots__
        """
469
        added_slot_attrs = ["name"]
dboe's avatar
dboe committed
470
471
        n_np = 5  # number of numpy array states
        n_old = len(valid_slot_attrs) - len(state[n_np:])
472
473
474
        if n_old > 0:
            for latest_index in range(n_old):
                new_slot = added_slot_attrs[-latest_index]
475
476
477
478
479
480
                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__.".format(**locals())
                )
481
482
483
484
                valid_slot_attrs.pop(valid_slot_attrs.index(new_slot))
                setattr(self, new_slot, None)

        for slot_index, slot in enumerate(valid_slot_attrs):
dboe's avatar
dboe committed
485
            state_index = n_np + slot_index
486
            setattr(self, slot, state[state_index])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
487

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
488
489
490
491
492
493
494
495
    @property
    def bulk(self):
        """
        The pure ndarray version of the actual state
            -> nothing attached
        """
        return np.array(self)

496
497
    @classmethod
    @contextmanager
498
    def _bypass_setters(cls, *slots, empty_means_all=True, demand_existence=False):
499
500
501
        """
        Temporarily remove the setter in __slot_setters__ corresponding to slot
        position in __slot__. You should know what you do, when using this.
502
503
504
505
506

        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
507
508
            demand_existence (bool): if false do not check the existence of the
                slot in __slots__ - do nothing for that slot. Handle with care!
509
510
511
512
513
514
        """
        if not slots and empty_means_all:
            slots = cls.__slots__
        slot_indices = []
        setters = []
        for slot in slots:
515
            slot_index = cls.__slots__.index(slot) if slot in cls.__slots__ else None
dboe's avatar
dboe committed
516
517
518
            if slot_index is None:
                # slot not in cls.__slots__.
                if demand_existence:
519
                    raise ValueError("Slot {slot} not existing".format(**locals()))
dboe's avatar
dboe committed
520
                continue
521
522
523
524
525
526
527
            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
528
        yield
529
530
        for slot_index, setter in zip(slot_indices, setters):
            cls.__slot_setters__[slot_index] = setter
531

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
532
533
534
    def copy(self, *args, **kwargs):
        """
        The standard ndarray copy does not copy slots. Correct for this.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
535

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
536
537
        Examples:
            >>> import tfields
dboe's avatar
dboe committed
538
539
            >>> m = tfields.TensorMaps(
            ...     [[1,2,3], [3,3,3], [0,0,0], [5,6,7]],
dboe's avatar
dboe committed
540
            ...     [[1], [3], [0], [5]],
541
542
            ...     maps=[
            ...         ([[0, 1, 2], [1, 2, 3]], [21, 42]),
dboe's avatar
dboe committed
543
544
            ...         [[1]],
            ...         [[0, 1, 2, 3]]
545
            ...     ])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
546
            >>> mc = m.copy()
dboe's avatar
dboe committed
547
548
            >>> mc.equal(m)
            True
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
549
550
            >>> mc is m
            False
dboe's avatar
dboe committed
551
552
553
554
            >>> mc.fields is m.fields
            False
            >>> mc.fields[0] is m.fields[0]
            False
dboe's avatar
dboe committed
555
            >>> mc.maps[3].fields[0] is m.maps[3].fields[0]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
556
557
558
            False

        """
dboe's avatar
dboe committed
559
560
        # works with __reduce__ / __setstate__
        return deepcopy(self)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
561
562
563
564
565


class Tensors(AbstractNdarray):
    """
    Set of tensors with the same basis.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
566

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
567
568
    TODO:
        all slot args should be protected -> _base
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
569

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
570
571
    Args:
        tensors: np.ndarray or AbstractNdarray subclass
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
572
573
        **kwargs:
            name: optional - custom name, can be anything
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
574

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
575
576
    Examples:
        >>> import numpy as np
577
        >>> import tfields
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
578
579

        Initialize a scalar range
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
580

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
581
582
583
584
585
        >>> scalars = tfields.Tensors([0, 1, 2])
        >>> scalars.rank == 0
        True

        Initialize vectors
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
586

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
587
588
589
590
591
        >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
        >>> vectors.rank == 1
        True
        >>> vectors.dim == 3
        True
592
        >>> assert vectors.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
593
594

        Initialize the Levi-Zivita Tensor
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
595

596
597
598
599
        >>> 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
600
601
602
603
604
605
606
607
        >>> 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
608

dboe's avatar
dboe committed
609
610
        >>> cyl = tfields.Tensors([[5, np.arctan(4. / 3.), 42]],
        ...                       coord_sys='cylinder')
611
        >>> assert cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
612
        >>> cyl.transform('cartesian')
613
        >>> assert cyl.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
614
615
616
617
618
619
        >>> 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
620

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
621
622
        >>> with vectors.tmp_transform('cylinder'):
        ...     vect_cyl = tfields.Tensors(vectors)
623
624
        ...     assert vect_cyl.coord_sys == vectors.coord_sys
        >>> assert vect_cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
625
626

        You can demand a special dimension.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
627

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
628
629
630
631
632
633
634
635
        >>> _ = 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
636

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
637
638
639
640
641
642
643
644
        >>> _ = 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)

    """
645
646
647

    __slots__ = ["coord_sys", "name"]
    __slot_defaults__ = ["cartesian"]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
648
649
650
    __slot_setters__ = [tfields.bases.get_coord_system_name]

    def __new__(cls, tensors, **kwargs):
dboe's avatar
dboe committed
651
652
653
        dtype = kwargs.pop("dtype", None)
        order = kwargs.pop("order", None)
        dim = kwargs.pop("dim", None)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
654

dboe's avatar
dboe committed
655
        """ copy constructor extracts the kwargs from tensors"""
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
656
657
658
        if issubclass(type(tensors), Tensors):
            if dim is not None:
                dim = tensors.dim
dboe's avatar
dboe committed
659
            coord_sys = kwargs.pop("coord_sys", tensors.coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
660
            tensors = tensors.copy()
661
            tensors.transform(coord_sys)
662
663
            kwargs["coord_sys"] = coord_sys
            kwargs["name"] = kwargs.pop("name", tensors.name)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
664
665
666
667
            if dtype is None:
                dtype = tensors.dtype
        else:
            if dtype is None:
dboe's avatar
dboe committed
668
                if hasattr(tensors, "dtype"):
669
670
671
                    dtype = tensors.dtype
                else:
                    dtype = np.float64
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
672

dboe's avatar
dboe committed
673
        """ demand iterable structure """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
674
675
        try:
            len(tensors)
dboe's avatar
dboe committed
676
        except TypeError:
dboe's avatar
dboe committed
677
            raise TypeError(
678
                "Iterable structure necessary." " Got {tensors}".format(**locals())
dboe's avatar
dboe committed
679
            )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
680

dboe's avatar
dboe committed
681
        """ process empty inputs """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
682
683
684
685
686
687
688
689
        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
690
            elif hasattr(tensors, "shape"):
dboe's avatar
dboe committed
691
                dim = dim(tensors)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
692
            else:
693
                raise ValueError("Empty tensors need dimension parameter 'dim'.")
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
694
695
696
697

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

dboe's avatar
dboe committed
698
        """ check dimension(s) """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
699
700
        for d in obj.shape[1:]:
            if not d == obj.dim:
dboe's avatar
dboe committed
701
702
703
704
705
706
707
                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
708
709
        if dim is not None:
            if dim != obj.dim:
dboe's avatar
dboe committed
710
711
712
713
                raise ValueError(
                    "Incorrect dimension: {obj.dim} given,"
                    " {dim} demanded.".format(**locals())
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
714

dboe's avatar
dboe committed
715
        """ update kwargs with defaults from slots """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
716
717
        cls._update_slot_kwargs(kwargs)

dboe's avatar
dboe committed
718
        """ set kwargs to slots attributes """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
719
720
        for attr in kwargs:
            if attr not in cls._iter_slots():
dboe's avatar
dboe committed
721
722
723
724
                raise AttributeError(
                    "Keyword argument {attr} not accepted "
                    "for class {cls}".format(**locals())
                )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
725
726
727
728
            setattr(obj, attr, kwargs[attr])

        return obj

729
730
731
732
    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
733

734
735
736
        Examples:
            >>> import tfields
            >>> vectors = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
dboe's avatar
dboe committed
737
738
            >>> scalar_field = tfields.TensorFields(
            ...     vectors, [42, 21, 10.5], [1, 2, 3])
739
740
741
742
743
744
745
            >>> [(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
746
747
748
749
    @classmethod
    def merged(cls, *objects, **kwargs):
        """
        Factory method
dboe's avatar
dboe committed
750
        Merges all input arguments to one object
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
751

752
753
754
        Args:
            return_templates (bool): return the templates which can be used
                together with cut to retrieve the original objects
dboe's avatar
dboe committed
755
756
            dim (int):
            **kwargs: passed to cls
757

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
758
759
760
761
762
        Examples:
            >>> import numpy as np
            >>> import tfields
            >>> import tfields.bases

763
764
            The new object with turn out in the most frequent coordinate
            system if not specified explicitly
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
765

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
766
            >>> vec_a = tfields.Tensors([[0, 0, 0], [0, 0, 1], [0, -1, 0]])
dboe's avatar
dboe committed
767
768
769
770
771
772
            >>> 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]])
773
            >>> assert merge.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
774
775
776
777
778
779
780
781
            >>> 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
782

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
783
784
            >>> tm_a = tfields.TensorMaps(merge, maps=[[[0, 1, 2]]])
            >>> tm_b = tm_a.copy()
785
            >>> assert tm_a.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
786
            >>> tm_merge = tfields.TensorMaps.merged(tm_a, tm_b)
787
            >>> assert tm_merge.coord_sys == 'cylinder'
dboe's avatar
dboe committed
788
            >>> assert tm_merge.maps[3].equal([[0, 1, 2],
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
789
790
791
            ...                               list(range(len(merge),
            ...                                          len(merge) + 3,
            ...                                          1))])
dboe's avatar
dboe committed
792

793
794
            >>> obj_list = [tfields.Tensors([[1, 2, 3]],
            ...             coord_sys=tfields.bases.CYLINDER),
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
795
796
            ...             tfields.Tensors([[3] * 3]),
            ...             tfields.Tensors([[5, 1, 3]])]
797
798
            >>> merge2 = tfields.Tensors.merged(
            ...     *obj_list, coord_sys=tfields.bases.CARTESIAN)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
799
800
            >>> assert merge2.equal([[-0.41614684, 0.90929743, 3.],
            ...                      [3, 3, 3], [5, 1, 3]], atol=1e-8)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
801

802
803
804
805
806
807
808
809
810
            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
811
812
        """

dboe's avatar
dboe committed
813
814
        """ get most frequent coord_sys or predefined coord_sys """
        coord_sys = kwargs.get("coord_sys", None)
815
        return_templates = kwargs.pop("return_templates", False)
816
        if coord_sys is None:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
817
818
819
            bases = []
            for t in objects:
                try:
820
                    bases.append(t.coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
821
822
823
                except AttributeError:
                    pass
            if bases:
824
                # get most frequent coord_sys
825
                coord_sys = sorted(bases, key=Counter(bases).get, reverse=True)[0]
dboe's avatar
dboe committed
826
                kwargs["coord_sys"] = coord_sys
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
827
            else:
828
                default = cls.__slot_defaults__[cls.__slots__.index("coord_sys")]
dboe's avatar
dboe committed
829
                kwargs["coord_sys"] = default
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
830

dboe's avatar
dboe committed
831
        """ transform all raw inputs to cls type with correct coord_sys. Also
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
832
        automatically make a copy of those instances that are of the correct
dboe's avatar
dboe committed
833
        type already."""
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
834
        objects = [cls.__new__(cls, t, **kwargs) for t in objects]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
835

dboe's avatar
dboe committed
836
        """ check rank and dimension equality """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
837
838
839
840
841
        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
842
        """ merge all objects """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
843
844
845
846
847
848
        remainingObjects = objects[1:] or []
        tensors = objects[0]

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

849
        if len(tensors) == 0 and not kwargs.get("dim", None):
850
851
            # if you can not determine the tensor dimension, search for the
            # first object with some entries
852
            kwargs["dim"] = dim(objects[0])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
853

854
        inst = cls.__new__(cls, tensors, **kwargs)
855
        if not return_templates:
856
            return inst
857
858
        else:
            tensor_lengths = [len(o) for o in objects]
859
            cum_tensor_lengths = [sum(tensor_lengths[:i]) for i in range(len(objects))]
860
861
            templates = [
                tfields.TensorFields(
862
                    np.empty((len(obj), 0)),
863
864
865
866
                    np.arange(tensor_lengths[i]) + cum_tensor_lengths[i],
                )
                for i, obj in enumerate(objects)
            ]
867
            return inst, templates
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
868
869
870
871
872

    @classmethod
    def grid(cls, *base_vectors, **kwargs):
        """
        Args:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
873
874
875
876
877
878
879
            *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
880

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
881
882
883
884
885
886
                    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
887
888
889

        Examples:
            Initilaize using the mgrid notation
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
890

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
891
892
893
894
895
896
897
898
899
900
901
            >>> 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
902
903
904

            Lists or arrays are accepted also.
            Furthermore, the iteration order can be changed
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
905

dboe's avatar
dboe committed
906
907
908
            >>> 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
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
            >>> 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
932
933
            When given the coord_sys argument, the grid is performed in the
            given coorinate system:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
934

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
935
936
937
938
939
940
941
942
943
            >>> 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
944
        """
dboe's avatar
dboe committed
945
        cls_kwargs = {
946
            attr: kwargs.pop(attr) for attr in list(kwargs) if attr in cls.__slots__
dboe's avatar
dboe committed
947
948
949
950
        }
        inst = cls.__new__(
            cls, tfields.lib.grid.igrid(*base_vectors, **kwargs), **cls_kwargs
        )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
        return inst

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

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

967
    def transform(self, coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
968
969
        """
        Args:
970
            coord_sys (str)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
971
972
973
974
975
976

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

            CARTESIAN to SPHERICAL
dboe's avatar
dboe committed
977
978
            >>> 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
979
980
981
            >>> t.transform('spherical')

            r
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
982

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
983
984
985
            >>> assert t[0, 0] == 3

            phi
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
986

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
987
988
989
990
            >>> 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
991

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
992
993
994
995
996
            >>> 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
997

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
998
999
1000
1001
1002
            >>> assert t[4, 0] == 0.
            >>> assert t[4, 2] == 0.


            CARTESIAN to CYLINDER
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1003

dboe's avatar
dboe committed
1004
1005
            >>> 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
1006
1007
            >>> t_cyl = tCart.copy()
            >>> t_cyl.transform('cylinder')
1008
            >>> assert t_cyl.coord_sys == 'cylinder'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1009
1010

            R
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1011

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1012
1013
1014
1015
1016
1017
            >>> 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
1018

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1019
1020
1021
1022
1023
1024
            >>> 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
1025

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1026
1027
1028
1029
            >>> assert t_cyl[0, 2] == 42
            >>> assert t_cyl[2, 2] == -1

            >>> t_cyl.transform('cartesian')
1030
            >>> assert t_cyl.coord_sys == 'cartesian'
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1031
1032
1033
1034
            >>> assert t_cyl[0, 0] == 3

        """
        #           scalars                 empty             already there
1035
1036
        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
1037
1038
            return

1039
1040
1041
        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
1042
1043

    @contextmanager
1044
    def tmp_transform(self, coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1045
        """
1046
        Temporarily change the coord_sys to another coord_sys and change it back at exit
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1047
1048
        This method is for cleaner code only.
        No speed improvements go with this.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1049

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1050
1051
        Args:
            see transform
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1052

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1053
1054
        Examples:
            >>> import tfields
1055
            >>> p = tfields.Tensors([[1,2,3]], coord_sys=tfields.bases.SPHERICAL)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1056
            >>> with p.tmp_transform(tfields.bases.CYLINDER):
1057
1058
            ...     assert p.coord_sys == tfields.bases.CYLINDER
            >>> assert p.coord_sys == tfields.bases.SPHERICAL
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1059
1060

        """
1061
1062
        baseBefore = self.coord_sys
        if baseBefore == coord_sys:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1063
1064
            yield
        else:
1065
            self.transform(coord_sys)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1066
1067
1068
1069
1070
1071
1072
1073

            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
1074

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1075
1076
        Args:
            coordinate (int): coordinate index
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1077

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1078
1079
1080
1081
1082
1083
        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
1084
1085
            multiple coordinates can be mirrored at the same time
            i.e. a point mirrorion would be
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1086

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1087
1088
1089
1090
1091
            >>> 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
1092
1093
            The mirroring will only be applied to the points meeting the
            condition.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1094

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1095
1096
            >>> import sympy
            >>> x, y, z = sympy.symbols('x y z')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1097
            >>> p.mirror([0, 2], y > 3)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
            >>> 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
1108
                self.mirror(c, condition=condition)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1109
1110
1111
1112
1113
        elif isinstance(coordinate, int):
            self[:, coordinate][condition] *= -1
        else:
            raise TypeError()

dboe's avatar
dboe committed
1114
1115
1116
1117
1118
1119
1120
1121
1122
    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
1123
1124
1125
1126
1127
        """
        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
1128

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1129
1130
1131
1132
1133
1134
        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
1135
            coord_sys (str or sympy.CoordinateSystem): in which coord sys the
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1136
                transformation should be done
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1137

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1138
1139
1140
1141
1142
        Examples:
            >>> import tfields
            >>> import numpy as np
            >>> pStart = tfields.Points3D([[6, 2 * np.pi, 1],
            ...                            [6, 2 * np.pi / 5 * 3, 1]],
1143
            ...                           coord_sys='cylinder')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
            >>> 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))

1156
1157
1158
        if coord_sys is None:
            coord_sys = self.coord_sys
        with self.tmp_transform(coord_sys):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1159
            # map all values to first segment
dboe's avatar
dboe committed
1160
1161
1162
1163
1164
            self[:, coordinate] = (
                (self[:, coordinate] - offset) % (periodicity / num_segments)
                + offset
                + segment * periodicity / num_segments
            )
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1165

1166
    def equal(self, other, rtol=None, atol=None, equal_nan=False, return_bool=True):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1167
1168
        """
        Evaluate, whether the instance has the same content as other.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1169

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1170
1171
1172
1173
1174
1175
1176
        Args:
            optional:
                rtol (float)
                atol (float)
                equal_nan (bool)
            see numpy.isclose
        """
1177
        if issubclass(type(other), Tensors) and self.coord_sys != other.coord_sys:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1178
            other = other.copy()
1179