field.py 42.5 KB
Newer Older
1
import functools
Martin Bauer's avatar
Martin Bauer committed
2
import hashlib
3
import operator
Martin Bauer's avatar
Martin Bauer committed
4
5
import pickle
import re
6
from enum import Enum
7
from itertools import chain
Martin Bauer's avatar
Martin Bauer committed
8
9
from typing import List, Optional, Sequence, Set, Tuple

10
11
12
import numpy as np
import sympy as sp
from sympy.core.cache import cacheit
Martin Bauer's avatar
Martin Bauer committed
13

14
import pystencils
15
from pystencils.alignedarray import aligned_empty
16
from pystencils.data_types import StructType, TypedSymbol, create_type
17
from pystencils.kernelparameters import FieldShapeSymbol, FieldStrideSymbol
Martin Bauer's avatar
Martin Bauer committed
18
from pystencils.stencil import direction_string_to_offset, offset_to_direction_string
Martin Bauer's avatar
Martin Bauer committed
19
from pystencils.sympyextensions import is_integer_sequence
20

21
__all__ = ['Field', 'fields', 'FieldType', 'AbstractField']
Martin Bauer's avatar
Martin Bauer committed
22

23

24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
class FieldType(Enum):
    # generic fields
    GENERIC = 0
    # index fields are currently only used for boundary handling
    # the coordinates are not the loop counters in that case, but are read from this index field
    INDEXED = 1
    # communication buffer, used for (un)packing data in communication.
    BUFFER = 2
    # unsafe fields may be accessed in an absolute fashion - the index depends on the data
    # and thus may lead to out-of-bounds accesses
    CUSTOM = 3
    # staggered field
    STAGGERED = 4

    @staticmethod
    def is_generic(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.GENERIC

    @staticmethod
    def is_indexed(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.INDEXED

    @staticmethod
    def is_buffer(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.BUFFER

    @staticmethod
    def is_custom(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.CUSTOM

    @staticmethod
    def is_staggered(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.STAGGERED


def fields(description=None, index_dimensions=0, layout=None, field_type=FieldType.GENERIC, **kwargs):
65
66
67
    """Creates pystencils fields from a string description.

    Examples:
Martin Bauer's avatar
Martin Bauer committed
68
69
70
71
        Create a 2D scalar and vector field:
            >>> s, v = fields("s, v(2): double[2D]")
            >>> assert s.spatial_dimensions == 2 and s.index_dimensions == 0
            >>> assert (v.spatial_dimensions, v.index_dimensions, v.index_shape) == (2, 1, (2,))
72

Martin Bauer's avatar
Martin Bauer committed
73
74
75
76
        Create an integer field of shape (10, 20):
            >>> f = fields("f : int32[10, 20]")
            >>> f.has_fixed_shape, f.shape
            (True, (10, 20))
77

Martin Bauer's avatar
Martin Bauer committed
78
79
80
81
82
        Numpy arrays can be used as template for shape and data type of field:
            >>> arr_s, arr_v = np.zeros([20, 20]), np.zeros([20, 20, 2])
            >>> s, v = fields("s, v(2)", s=arr_s, v=arr_v)
            >>> assert s.index_dimensions == 0 and s.dtype.numpy_dtype == arr_s.dtype
            >>> assert v.index_shape == (2,)
83

Martin Bauer's avatar
Martin Bauer committed
84
85
86
87
88
89
90
91
92
93
        Format string can be left out, field names are taken from keyword arguments.
            >>> fields(f1=arr_s, f2=arr_s)
            [f1, f2]

        The keyword names ``index_dimension`` and ``layout`` have special meaning, don't use them for field names
            >>> f = fields(f=arr_v, index_dimensions=1)
            >>> assert f.index_dimensions == 1
            >>> f = fields("pdfs(19) : float32[3D]", layout='fzyx')
            >>> f.layout
            (2, 1, 0)
94
95
96
97
98
99
100
101
102
103
    """
    result = []
    if description:
        field_descriptions, dtype, shape = _parse_description(description)
        layout = 'numpy' if layout is None else layout
        for field_name, idx_shape in field_descriptions:
            if field_name in kwargs:
                arr = kwargs[field_name]
                idx_shape_of_arr = () if not len(idx_shape) else arr.shape[-len(idx_shape):]
                assert idx_shape_of_arr == idx_shape
Michael Kuron's avatar
Michael Kuron committed
104
                f = Field.create_from_numpy_array(field_name, kwargs[field_name], index_dimensions=len(idx_shape),
105
                                                  field_type=field_type)
106
107
            elif isinstance(shape, tuple):
                f = Field.create_fixed_size(field_name, shape + idx_shape, dtype=dtype,
108
                                            index_dimensions=len(idx_shape), layout=layout, field_type=field_type)
109
110
            elif isinstance(shape, int):
                f = Field.create_generic(field_name, spatial_dimensions=shape, dtype=dtype,
111
                                         index_shape=idx_shape, layout=layout, field_type=field_type)
112
113
            elif shape is None:
                f = Field.create_generic(field_name, spatial_dimensions=2, dtype=dtype,
114
                                         index_shape=idx_shape, layout=layout, field_type=field_type)
115
116
117
118
119
120
            else:
                assert False
            result.append(f)
    else:
        assert layout is None, "Layout can not be specified when creating Field from numpy array"
        for field_name, arr in kwargs.items():
Michael Kuron's avatar
Michael Kuron committed
121
            result.append(Field.create_from_numpy_array(field_name, arr, index_dimensions=index_dimensions,
122
                                                        field_type=field_type))
123
124
125
126
127
128
129
130
131

    if len(result) == 0:
        return None
    elif len(result) == 1:
        return result[0]
    else:
        return result


132
133
134
135
136
137
138
class AbstractField:

    class AbstractAccess:
        pass


class Field(AbstractField):
139
140
141
142
    """
    With fields one can formulate stencil-like update rules on structured grids.
    This Field class knows about the dimension, memory layout (strides) and optionally about the size of an array.

Martin Bauer's avatar
Martin Bauer committed
143
    Creating Fields:
Martin Bauer's avatar
Martin Bauer committed
144
145
        The preferred method to create fields is the `fields` function.
        Alternatively one can use one of the static functions `Field.create_generic`, `Field.create_from_numpy_array`
146
        and `Field.create_fixed_size`. Don't instantiate the Field directly!
Martin Bauer's avatar
Martin Bauer committed
147
148
149
150
151
        Fields can be created with known or unknown shapes:

        1. If you want to create a kernel with fixed loop sizes i.e. the shape of the array is already known.
           This is usually the case if just-in-time compilation directly from Python is done.
           (see `Field.create_from_numpy_array`
152
        2. create a more general kernel that works for variable array sizes. This can be used to create kernels
Martin Bauer's avatar
Martin Bauer committed
153
           beforehand for a library. (see `Field.create_generic`)
154

Martin Bauer's avatar
Martin Bauer committed
155
    Dimensions and Indexing:
156
157
        A field has spatial and index dimensions, where the spatial dimensions come first.
        The interpretation is that the field has multiple cells in (usually) two or three dimensional space which are
Martin Bauer's avatar
Martin Bauer committed
158
        looped over. Additionally N values are stored per cell. In this case spatial_dimensions is two or three,
Martin Bauer's avatar
Martin Bauer committed
159
        and index_dimensions equals N. If you want to store a matrix on each point in a two dimensional grid, there
Martin Bauer's avatar
Martin Bauer committed
160
        are four dimensions, two spatial and two index dimensions: ``len(arr.shape) == spatial_dims + index_dims``
161

Martin Bauer's avatar
Martin Bauer committed
162
163
164
165
166
        The shape of the index dimension does not have to be specified. Just use the 'index_dimensions' parameter.
        However, it is good practice to define the shape, since out of bounds accesses can be directly detected in this
        case. The shape can be passed with the 'index_shape' parameter of the field creation functions.

        When accessing (indexing) a field the result is a `Field.Access` which is derived from sympy Symbol.
Martin Bauer's avatar
Martin Bauer committed
167
        First specify the spatial offsets in [], then in case index_dimension>0 the indices in ()
Martin Bauer's avatar
Martin Bauer committed
168
        e.g. ``f[-1,0,0](7)``
169

Michael Kuron's avatar
Michael Kuron committed
170
171
172
173
174
175
176
177
    Staggered Fields:
        Staggered fields are used to store a value on a second grid shifted by half a cell with respect to the usual
        grid.

        The first index dimension is used to specify the position on the staggered grid (e.g. 0 means half-way to the
        eastern neighbor, 1 is half-way to the northern neighbor, etc.), while additional indices can be used to store
        multiple values at each position.

Martin Bauer's avatar
Martin Bauer committed
178
    Example using no index dimensions:
179
        >>> a = np.zeros([10, 10])
Martin Bauer's avatar
Martin Bauer committed
180
        >>> f = Field.create_from_numpy_array("f", a, index_dimensions=0)
Martin Bauer's avatar
Martin Bauer committed
181
        >>> jacobi = (f[-1,0] + f[1,0] + f[0,-1] + f[0,1]) / 4
182

Martin Bauer's avatar
Martin Bauer committed
183
    Examples for index dimensions to create LB field and implement stream pull:
Martin Bauer's avatar
Martin Bauer committed
184
        >>> from pystencils import Assignment
185
        >>> stencil = np.array([[0,0], [0,1], [0,-1]])
Martin Bauer's avatar
Martin Bauer committed
186
        >>> src, dst = fields("src(3), dst(3) : double[2D]")
187
        >>> assignments = [Assignment(dst[0,0](i), src[-offset](i)) for i, offset in enumerate(stencil)];
188
    """
189
190

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
191
    def create_generic(field_name, spatial_dimensions, dtype=np.float64, index_dimensions=0, layout='numpy',
192
                       index_shape=None, field_type=FieldType.GENERIC) -> 'Field':
193
194
195
        """
        Creates a generic field where the field size is not fixed i.e. can be called with arrays of different sizes

Martin Bauer's avatar
Martin Bauer committed
196
197
198
199
200
201
202
        Args:
            field_name: symbolic name for the field
            dtype: numpy data type of the array the kernel is called with later
            spatial_dimensions: see documentation of Field
            index_dimensions: see documentation of Field
            layout: tuple specifying the loop ordering of the spatial dimensions e.g. (2, 1, 0 ) means that
                    the outer loop loops over dimension 2, the second outer over dimension 1, and the inner loop
Martin Bauer's avatar
Martin Bauer committed
203
                    over dimension 0. Also allowed: the strings 'numpy' (0,1,..d) or 'reverse_numpy' (d, ..., 1, 0)
Martin Bauer's avatar
Martin Bauer committed
204
205
206
            index_shape: optional shape of the index dimensions i.e. maximum values allowed for each index dimension,
                        has to be a list or tuple
            field_type: besides the normal GENERIC fields, there are INDEXED fields that store indices of the domain
207
208
209
                        that should be iterated over, BUFFER fields that are used to generate communication
                        packing/unpacking kernels, and STAGGERED fields, which store values half-way to the next
                        cell
210
        """
211
212
213
        if index_shape is not None:
            assert index_dimensions == 0 or index_dimensions == len(index_shape)
            index_dimensions = len(index_shape)
214
        if isinstance(layout, str):
Martin Bauer's avatar
Martin Bauer committed
215
            layout = spatial_layout_string_to_tuple(layout, dim=spatial_dimensions)
216

Martin Bauer's avatar
Martin Bauer committed
217
218
        total_dimensions = spatial_dimensions + index_dimensions
        if index_shape is None or len(index_shape) == 0:
219
            shape = tuple([FieldShapeSymbol([field_name], i) for i in range(total_dimensions)])
220
        else:
221
            shape = tuple([FieldShapeSymbol([field_name], i) for i in range(spatial_dimensions)] + list(index_shape))
222

223
        strides = tuple([FieldStrideSymbol(field_name, i) for i in range(total_dimensions)])
224

Martin Bauer's avatar
Martin Bauer committed
225
226
227
        np_data_type = np.dtype(dtype)
        if np_data_type.fields is not None:
            if index_dimensions != 0:
228
229
230
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)
231
        if field_type == FieldType.STAGGERED and index_dimensions == 0:
Michael Kuron's avatar
Michael Kuron committed
232
            raise ValueError("A staggered field needs at least one index dimension")
233

234
        return Field(field_name, field_type, dtype, layout, shape, strides)
235

236
    @staticmethod
Michael Kuron's avatar
Michael Kuron committed
237
    def create_from_numpy_array(field_name: str, array: np.ndarray, index_dimensions: int = 0,
238
                                field_type=FieldType.GENERIC) -> 'Field':
Martin Bauer's avatar
Martin Bauer committed
239
240
        """Creates a field based on the layout, data type, and shape of a given numpy array.

241
        Kernels created for these kind of fields can only be called with arrays of the same layout, shape and type.
Martin Bauer's avatar
Martin Bauer committed
242
243
244
245
246

        Args:
            field_name: symbolic name for the field
            array: numpy array
            index_dimensions: see documentation of Field
247
            field_type: kind of field
248
        """
Martin Bauer's avatar
Martin Bauer committed
249
250
        spatial_dimensions = len(array.shape) - index_dimensions
        if spatial_dimensions < 1:
251
252
            raise ValueError("Too many index dimensions. At least one spatial dimension required")

Martin Bauer's avatar
Martin Bauer committed
253
254
255
        full_layout = get_layout_of_array(array)
        spatial_layout = tuple([i for i in full_layout if i < spatial_dimensions])
        assert len(spatial_layout) == spatial_dimensions
256

Martin Bauer's avatar
Martin Bauer committed
257
258
        strides = tuple([s // np.dtype(array.dtype).itemsize for s in array.strides])
        shape = tuple(int(s) for s in array.shape)
259

Martin Bauer's avatar
Martin Bauer committed
260
261
262
        numpy_dtype = np.dtype(array.dtype)
        if numpy_dtype.fields is not None:
            if index_dimensions != 0:
263
264
265
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)
266
        if field_type == FieldType.STAGGERED and index_dimensions == 0:
Michael Kuron's avatar
Michael Kuron committed
267
            raise ValueError("A staggered field needs at least one index dimension")
268

269
        return Field(field_name, field_type, array.dtype, spatial_layout, shape, strides)
270
271

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
272
    def create_fixed_size(field_name: str, shape: Tuple[int, ...], index_dimensions: int = 0,
Michael Kuron's avatar
Michael Kuron committed
273
                          dtype=np.float64, layout: str = 'numpy', strides: Optional[Sequence[int]] = None,
274
                          field_type=FieldType.GENERIC) -> 'Field':
275
        """
276
        Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout
277

Martin Bauer's avatar
Martin Bauer committed
278
279
280
281
282
283
284
        Args:
            field_name: symbolic name for the field
            shape: overall shape of the array
            index_dimensions: how many of the trailing dimensions are interpreted as index (as opposed to spatial)
            dtype: numpy data type of the array the kernel is called with later
            layout: full layout of array, not only spatial dimensions
            strides: strides in bytes or None to automatically compute them from shape (assuming no padding)
285
            field_type: kind of field
286
        """
Martin Bauer's avatar
Martin Bauer committed
287
288
        spatial_dimensions = len(shape) - index_dimensions
        assert spatial_dimensions >= 1
289

290
        if isinstance(layout, str):
Martin Bauer's avatar
Martin Bauer committed
291
            layout = layout_string_to_tuple(layout, spatial_dimensions + index_dimensions)
292
293

        shape = tuple(int(s) for s in shape)
294
        if strides is None:
Martin Bauer's avatar
Martin Bauer committed
295
            strides = compute_strides(shape, layout)
296
297
298
        else:
            assert len(strides) == len(shape)
            strides = tuple([s // np.dtype(dtype).itemsize for s in strides])
299

Martin Bauer's avatar
Martin Bauer committed
300
301
302
        numpy_dtype = np.dtype(dtype)
        if numpy_dtype.fields is not None:
            if index_dimensions != 0:
303
304
305
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)
306
        if field_type == FieldType.STAGGERED and index_dimensions == 0:
Michael Kuron's avatar
Michael Kuron committed
307
            raise ValueError("A staggered field needs at least one index dimension")
308

Martin Bauer's avatar
Martin Bauer committed
309
310
311
        spatial_layout = list(layout)
        for i in range(spatial_dimensions, len(layout)):
            spatial_layout.remove(i)
312
        return Field(field_name, field_type, dtype, tuple(spatial_layout), shape, strides)
313

314
    def __init__(self, field_name, field_type, dtype, layout, shape, strides):
315
        """Do not use directly. Use static create* methods"""
316
        self._field_name = field_name
Martin Bauer's avatar
Martin Bauer committed
317
        assert isinstance(field_type, FieldType)
318
        assert len(shape) == len(strides)
Martin Bauer's avatar
Martin Bauer committed
319
        self.field_type = field_type
Martin Bauer's avatar
Martin Bauer committed
320
        self._dtype = create_type(dtype)
Martin Bauer's avatar
Martin Bauer committed
321
        self._layout = normalize_layout(layout)
322
323
        self.shape = shape
        self.strides = strides
324
        self.latex_name = None  # type: Optional[str]
325
326
327
328
        self.coordinate_origin = sp.Matrix(tuple(
            0 for _ in range(self.spatial_dimensions)
        ))  # type: tuple[float,sp.Symbol]
        self.coordinate_transform = sp.eye(self.spatial_dimensions)
329
330
        if field_type == FieldType.STAGGERED:
            assert self.staggered_stencil
331

Martin Bauer's avatar
Martin Bauer committed
332
    def new_field_with_different_name(self, new_name):
333
334
335
336
337
        if self.has_fixed_shape:
            return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
        else:
            return Field.create_generic(new_name, self.spatial_dimensions, self.dtype.numpy_dtype,
                                        self.index_dimensions, self._layout, self.index_shape, self.field_type)
338

339
    @property
Martin Bauer's avatar
Martin Bauer committed
340
    def spatial_dimensions(self) -> int:
341
342
343
        return len(self._layout)

    @property
Martin Bauer's avatar
Martin Bauer committed
344
    def index_dimensions(self) -> int:
345
        return len(self.shape) - len(self._layout)
346

347
348
349
350
    @property
    def ndim(self) -> int:
        return len(self.shape)

351
352
353
    def values_per_cell(self) -> int:
        return functools.reduce(operator.mul, self.index_shape, 1)

354
355
356
357
358
    @property
    def layout(self):
        return self._layout

    @property
Martin Bauer's avatar
Martin Bauer committed
359
    def name(self) -> str:
360
        return self._field_name
361
362

    @property
Martin Bauer's avatar
Martin Bauer committed
363
364
    def spatial_shape(self) -> Tuple[int, ...]:
        return self.shape[:self.spatial_dimensions]
365

366
    @property
Martin Bauer's avatar
Martin Bauer committed
367
    def has_fixed_shape(self):
Martin Bauer's avatar
Martin Bauer committed
368
        return is_integer_sequence(self.shape)
369

370
    @property
Martin Bauer's avatar
Martin Bauer committed
371
372
    def index_shape(self):
        return self.shape[self.spatial_dimensions:]
373

374
    @property
Martin Bauer's avatar
Martin Bauer committed
375
376
    def has_fixed_index_shape(self):
        return is_integer_sequence(self.index_shape)
377

378
    @property
Martin Bauer's avatar
Martin Bauer committed
379
380
    def spatial_strides(self):
        return self.strides[:self.spatial_dimensions]
381
382

    @property
Martin Bauer's avatar
Martin Bauer committed
383
384
    def index_strides(self):
        return self.strides[self.spatial_dimensions:]
385
386
387
388
389

    @property
    def dtype(self):
        return self._dtype

390
391
392
393
    @property
    def itemsize(self):
        return self.dtype.numpy_dtype.itemsize

394
    def __repr__(self):
395
        return self._field_name
396

Martin Bauer's avatar
Martin Bauer committed
397
398
399
400
    def neighbor(self, coord_id, offset):
        offset_list = [0] * self.spatial_dimensions
        offset_list[coord_id] = offset
        return Field.Access(self, tuple(offset_list))
401

402
    def neighbors(self, stencil):
403
        return [self.__getitem__(s) for s in stencil]
404

405
    @property
Martin Bauer's avatar
Martin Bauer committed
406
407
408
    def center_vector(self):
        index_shape = self.index_shape
        if len(index_shape) == 0:
409
410
            return sp.Matrix([self.center])
        if len(index_shape) == 1:
Martin Bauer's avatar
Martin Bauer committed
411
412
            return sp.Matrix([self(i) for i in range(index_shape[0])])
        elif len(index_shape) == 2:
413
414
415
            def cb(*args):
                r = self.__call__(*args)
                return r
Martin Bauer's avatar
Martin Bauer committed
416
            return sp.Matrix(*index_shape, cb)
417

418
    @property
419
    def center(self):
Martin Bauer's avatar
Martin Bauer committed
420
        center = tuple([0] * self.spatial_dimensions)
421
422
        return Field.Access(self, center)

423
424
425
426
    def __getitem__(self, offset):
        if type(offset) is np.ndarray:
            offset = tuple(offset)
        if type(offset) is str:
Martin Bauer's avatar
Martin Bauer committed
427
            offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
428
429
        if type(offset) is not tuple:
            offset = (offset,)
Martin Bauer's avatar
Martin Bauer committed
430
        if len(offset) != self.spatial_dimensions:
431
            raise ValueError("Wrong number of spatial indices: "
Martin Bauer's avatar
Martin Bauer committed
432
                             "Got %d, expected %d" % (len(offset), self.spatial_dimensions))
433
434
        return Field.Access(self, offset)

Martin Bauer's avatar
Martin Bauer committed
435
    def absolute_access(self, offset, index):
Martin Bauer's avatar
Martin Bauer committed
436
        assert FieldType.is_custom(self)
Martin Bauer's avatar
Martin Bauer committed
437
438
        return Field.Access(self, offset, index, is_absolute_access=True)

439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
    def interpolated_access(self,
                            offset: Tuple,
                            interpolation_mode='linear',
                            address_mode='BORDER',
                            allow_textures=True):
        """Provides access to field values at non-integer positions

        ``interpolated_access`` is similar to :func:`Field.absolute_access` except that
        it allows non-integer offsets and automatic handling of out-of-bound accesses.

        :param offset:              Tuple of spatial coordinates (can be floats)
        :param interpolation_mode:  One of :class:`pystencils.interpolation_astnodes.InterpolationMode`
        :param address_mode:        How boundaries are handled can be 'border', 'wrap', 'mirror', 'clamp'
        :param allow_textures:      Allow implementation by texture accesses on GPUs
        """
        from pystencils.interpolation_astnodes import Interpolator
        return Interpolator(self,
                            interpolation_mode,
                            address_mode,
                            allow_textures=allow_textures).at(offset)

Michael Kuron's avatar
Michael Kuron committed
460
461
462
463
464
465
466
    def staggered_access(self, offset, index=None):
        """If this field is a staggered field, it can be accessed using half-integer offsets.
        For example, an offset of ``(0, sp.Rational(1,2))`` or ``"E"`` corresponds to the staggered point to the east
        of the cell center, i.e. half-way to the eastern-next cell.
        If the field stores more than one value per staggered point (e.g. a vector or a tensor), the index (integer or
        tuple of integers) refers to which of these values to access.
        """
467
        assert FieldType.is_staggered(self)
Michael Kuron's avatar
Michael Kuron committed
468

469
        offset_orig = offset
Michael Kuron's avatar
Michael Kuron committed
470
471
472
473
474
475
476
477
478
479
480
481
        if type(offset) is np.ndarray:
            offset = tuple(offset)
        if type(offset) is str:
            offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
            offset = tuple([o * sp.Rational(1, 2) for o in offset])
        if type(offset) is not tuple:
            offset = (offset,)
        if len(offset) != self.spatial_dimensions:
            raise ValueError("Wrong number of spatial indices: "
                             "Got %d, expected %d" % (len(offset), self.spatial_dimensions))

        offset = list(offset)
482
        neighbor = [0] * len(offset)
Michael Kuron's avatar
Michael Kuron committed
483
484
485
        for i, o in enumerate(offset):
            if (o + sp.Rational(1, 2)).is_Integer:
                offset[i] += sp.Rational(1, 2)
486
487
                neighbor[i] = 1
        neighbor = offset_to_direction_string(neighbor)
488
489
490
491
492
        try:
            idx = self.staggered_stencil.index(neighbor)
        except ValueError:
            raise ValueError("{} is not a valid neighbor for the {} stencil".format(offset_orig,
                             self.staggered_stencil_name))
Michael Kuron's avatar
Michael Kuron committed
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
        offset = tuple(offset)

        if self.index_dimensions == 1:  # this field stores a scalar value at each staggered position
            if index is not None:
                raise ValueError("Cannot specify an index for a scalar staggered field")
            return Field.Access(self, offset, (idx,))
        else:  # this field stores a vector or tensor at each staggered position
            if index is None:
                raise ValueError("Wrong number of indices: "
                                 "Got %d, expected %d" % (0, self.index_dimensions - 1))
            if type(index) is np.ndarray:
                index = tuple(index)
            if type(index) is not tuple:
                index = (index,)
            if self.index_dimensions != len(index) + 1:
                raise ValueError("Wrong number of indices: "
                                 "Got %d, expected %d" % (len(index), self.index_dimensions - 1))

            return Field.Access(self, offset, (idx, *index))

513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
    @property
    def staggered_stencil(self):
        assert FieldType.is_staggered(self)
        stencils = {
            2: {
                2: ["E", "N"],  # D2Q5
                4: ["E", "N", "NE", "SE"]  # D2Q9
            },
            3: {
                3: ["E", "N", "T"],  # D3Q7
                7: ["E", "N", "T", "TNE", "BNE", "TSE", "BSE "],  # D3Q15
                9: ["E", "N", "T", "NE", "SE", "TE", "BE", "TN", "BN"],  # D3Q19
                13: ["E", "N", "T", "NE", "SE", "TE", "BE", "TN", "BN", "TNE", "BNE", "TSE", "BSE"]  # D3Q27
            }
        }
        if not self.index_shape[0] in stencils[self.spatial_dimensions]:
            raise ValueError("No known stencil has {} staggered points".format(self.index_shape[0]))
        return stencils[self.spatial_dimensions][self.index_shape[0]]

532
533
534
535
536
    @property
    def staggered_stencil_name(self):
        assert FieldType.is_staggered(self)
        return "D%dQ%d" % (self.spatial_dimensions, self.index_shape[0] * 2 + 1)

537
    def __call__(self, *args, **kwargs):
Martin Bauer's avatar
Martin Bauer committed
538
        center = tuple([0] * self.spatial_dimensions)
539
540
        return Field.Access(self, center)(*args, **kwargs)

541
    def hashable_contents(self):
542
543
        dth = hash(self._dtype)
        return self._layout, self.shape, self.strides, dth, self.field_type, self._field_name, self.latex_name
544

545
    def __hash__(self):
546
        return hash(self.hashable_contents())
547
548

    def __eq__(self, other):
549
550
        if not isinstance(other, Field):
            return False
551
        return self.hashable_contents() == other.hashable_contents()
552

553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
    @property
    def physical_coordinates(self):
        return self.coordinate_transform @ (self.coordinate_origin + pystencils.x_vector(self.spatial_dimensions))

    @property
    def physical_coordinates_staggered(self):
        return self.coordinate_transform @ \
            (self.coordinate_origin + pystencils.x_staggered_vector(self.spatial_dimensions))

    def index_to_physical(self, index_coordinates, staggered=False):
        if staggered:
            index_coordinates = sp.Matrix([i + 0.5 for i in index_coordinates])
        return self.coordinate_transform @ (self.coordinate_origin + index_coordinates)

    def physical_to_index(self, physical_coordinates, staggered=False):
        rtn = self.coordinate_transform.inv() @ physical_coordinates - self.coordinate_origin
        if staggered:
            rtn = sp.Matrix([i - 0.5 for i in rtn])

        return rtn

    def index_to_staggered_physical_coordinates(self, symbol_vector):
        symbol_vector += sp.Matrix([0.5] * self.spatial_dimensions)
        return self.create_physical_coordinates(symbol_vector)

    def set_coordinate_origin_to_field_center(self):
        self.coordinate_origin = -sp.Matrix([i / 2 for i in self.spatial_shape])

Martin Bauer's avatar
Martin Bauer committed
581
    # noinspection PyAttributeOutsideInit,PyUnresolvedReferences
582
    class Access(TypedSymbol, AbstractField.AbstractAccess):
Martin Bauer's avatar
Martin Bauer committed
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
        """Class representing a relative access into a `Field`.

        This class behaves like a normal sympy Symbol, it is actually derived from it. One can built up
        sympy expressions using field accesses, solve for them, etc.

        Examples:
            >>> vector_field_2d = fields("v(2): double[2D]")  # create a 2D vector field
            >>> northern_neighbor_y_component = vector_field_2d[0, 1](1)
            >>> northern_neighbor_y_component
            v_N^1
            >>> central_y_component = vector_field_2d(1)
            >>> central_y_component
            v_C^1
            >>> central_y_component.get_shifted(1, 0)  # move the existing access
            v_E^1
            >>> central_y_component.at_index(0)  # change component
            v_C^0
        """
601

602
603
604
605
        def __new__(cls, name, *args, **kwargs):
            obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
            return obj

606
        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False, dtype=None):
Martin Bauer's avatar
Martin Bauer committed
607
            field_name = field.name
Martin Bauer's avatar
Martin Bauer committed
608
            offsets_and_index = (*offsets, *idx) if idx is not None else offsets
Martin Bauer's avatar
Martin Bauer committed
609
            constant_offsets = not any([isinstance(o, sp.Basic) and not o.is_Integer for o in offsets_and_index])
610
611

            if not idx:
Martin Bauer's avatar
Martin Bauer committed
612
                idx = tuple([0] * field.index_dimensions)
613

Martin Bauer's avatar
Martin Bauer committed
614
615
616
            if constant_offsets:
                offset_name = offset_to_direction_string(offsets)
                if field.index_dimensions == 0:
617
                    superscript = None
Martin Bauer's avatar
Martin Bauer committed
618
                elif field.index_dimensions == 1:
619
                    superscript = str(idx[0])
620
                else:
Martin Bauer's avatar
Martin Bauer committed
621
622
623
624
                    idx_str = ",".join([str(e) for e in idx])
                    superscript = idx_str
                if field.has_fixed_index_shape and not isinstance(field.dtype, StructType):
                    for i, bound in zip(idx, field.index_shape):
625
626
                        if i >= bound:
                            raise ValueError("Field index out of bounds")
627
            else:
628
                offset_name = hashlib.md5(pickle.dumps(offsets_and_index)).hexdigest()[:12]
629
                superscript = None
630

Martin Bauer's avatar
Martin Bauer committed
631
            symbol_name = "%s_%s" % (field_name, offset_name)
632
            if superscript is not None:
Martin Bauer's avatar
Martin Bauer committed
633
                symbol_name += "^" + superscript
634

635
            obj = super(Field.Access, self).__xnew__(self, symbol_name, field.dtype)
636
637
638
639
640
641
642
            obj._field = field
            obj._offsets = []
            for o in offsets:
                if isinstance(o, sp.Basic):
                    obj._offsets.append(o)
                else:
                    obj._offsets.append(int(o))
643
            obj._offsets = tuple(obj._offsets)
Martin Bauer's avatar
Martin Bauer committed
644
            obj._offsetName = offset_name
645
            obj._superscript = superscript
646
647
            obj._index = idx

Martin Bauer's avatar
Martin Bauer committed
648
649
650
651
652
653
            obj._indirect_addressing_fields = set()
            for e in chain(obj._offsets, obj._index):
                if isinstance(e, sp.Basic):
                    obj._indirect_addressing_fields.update(a.field for a in e.atoms(Field.Access))

            obj._is_absolute_access = is_absolute_access
654
655
            return obj

656
        def __getnewargs__(self):
657
            return self.field, self.offsets, self.index, self.is_absolute_access, self.dtype
658

Martin Bauer's avatar
Martin Bauer committed
659
        # noinspection SpellCheckingInspection
660
        __xnew__ = staticmethod(__new_stage2__)
Martin Bauer's avatar
Martin Bauer committed
661
        # noinspection SpellCheckingInspection
662
663
664
        __xnew_cached_ = staticmethod(cacheit(__new_stage2__))

        def __call__(self, *idx):
Martin Bauer's avatar
Martin Bauer committed
665
            if self._index != tuple([0] * self.field.index_dimensions):
666
667
668
                raise ValueError("Indexing an already indexed Field.Access")

            idx = tuple(idx)
669

Martin Bauer's avatar
Martin Bauer committed
670
            if self.field.index_dimensions == 0 and idx == (0,):
671
672
                idx = ()

Martin Bauer's avatar
Martin Bauer committed
673
            if len(idx) != self.field.index_dimensions:
674
                raise ValueError("Wrong number of indices: "
Martin Bauer's avatar
Martin Bauer committed
675
                                 "Got %d, expected %d" % (len(idx), self.field.index_dimensions))
676
            return Field.Access(self.field, self._offsets, idx, dtype=self.dtype)
677

Martin Bauer's avatar
Martin Bauer committed
678
679
680
        def __getitem__(self, *idx):
            return self.__call__(*idx)

Martin Bauer's avatar
Martin Bauer committed
681
682
683
684
685
        def __iter__(self):
            """This is necessary to work with parts of sympy that test if an object is iterable (e.g. simplify).
            The __getitem__ would make it iterable"""
            raise TypeError("Field access is not iterable")

686
        @property
Martin Bauer's avatar
Martin Bauer committed
687
688
        def field(self) -> 'Field':
            """Field that the Access points to"""
689
690
691
            return self._field

        @property
Martin Bauer's avatar
Martin Bauer committed
692
693
        def offsets(self) -> Tuple:
            """Spatial offset as tuple"""
694
            return self._offsets
695

696
        @property
Martin Bauer's avatar
Martin Bauer committed
697
698
        def required_ghost_layers(self) -> int:
            """Largest spatial distance that is accessed."""
699
700
701
            return int(np.max(np.abs(self._offsets)))

        @property
Martin Bauer's avatar
Martin Bauer committed
702
        def nr_of_coordinates(self):
703
704
705
            return len(self._offsets)

        @property
Martin Bauer's avatar
Martin Bauer committed
706
        def offset_name(self) -> str:
Martin Bauer's avatar
Martin Bauer committed
707
708
709
710
711
712
713
            """Spatial offset as string, East-West for x, North-South for y and Top-Bottom for z coordinate.

            Example:
                >>> f = fields("f: double[2D]")
                >>> f[1, 1].offset_name  # north-east
                'NE'
            """
714
715
716
717
            return self._offsetName

        @property
        def index(self):
Martin Bauer's avatar
Martin Bauer committed
718
            """Value of index coordinates as tuple."""
719
720
            return self._index

721
        def neighbor(self, coord_id: int, offset: int) -> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
722
723
724
725
726
727
728
729
730
731
732
            """Returns a new Access with changed spatial coordinates.

            Args:
                coord_id: index of the coordinate to change (0 for x, 1 for y,...)
                offset: incremental change of this coordinate

            Example:
                >>> f = fields('f: [2D]')
                >>> f[0,0].neighbor(coord_id=1, offset=-1)
                f_S
            """
Martin Bauer's avatar
Martin Bauer committed
733
734
            offset_list = list(self.offsets)
            offset_list[coord_id] += offset
735
            return Field.Access(self.field, tuple(offset_list), self.index, dtype=self.dtype)
736

737
        def get_shifted(self, *shift) -> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
738
739
740
741
742
743
744
            """Returns a new Access with changed spatial coordinates

            Example:
                >>> f = fields("f: [2D]")
                >>> f[0,0].get_shifted(1, 1)
                f_NE
            """
745
746
747
748
            return Field.Access(self.field,
                                tuple(a + b for a, b in zip(shift, self.offsets)),
                                self.index,
                                dtype=self.dtype)
749

Martin Bauer's avatar
Martin Bauer committed
750
751
752
753
754
755
756
757
        def at_index(self, *idx_tuple) -> 'Field.Access':
            """Returns new Access with changed index.

            Example:
                >>> f = fields("f(9): [2D]")
                >>> f(0).at_index(8)
                f_C^8
            """
758
            return Field.Access(self.field, self.offsets, idx_tuple, dtype=self.dtype)
759

760
761
762
763
764
765
        def _eval_subs(self, old, new):
            return Field.Access(self.field,
                                tuple(sp.sympify(a).subs(old, new) for a in self.offsets),
                                tuple(sp.sympify(a).subs(old, new) for a in self.index),
                                dtype=self.dtype)

Martin Bauer's avatar
Martin Bauer committed
766
767
768
769
770
771
772
773
774
775
776
777
778
        @property
        def is_absolute_access(self) -> bool:
            """Indicates if a field access is relative to the loop counters (this is the default) or absolute"""
            return self._is_absolute_access

        @property
        def indirect_addressing_fields(self) -> Set['Field']:
            """Returns a set of fields that the access depends on.

             e.g. f[index_field[1, 0]], the outer access to f depends on index_field
             """
            return self._indirect_addressing_fields

779
        def _hashable_content(self):
780
781
            super_class_contents = super(Field.Access, self)._hashable_content()
            return (super_class_contents, self._field.hashable_contents(), *self._index, *self._offsets)
Martin Bauer's avatar
Martin Bauer committed
782

783
784
785
786
        def _staggered_offset(self, offsets, index):
            assert FieldType.is_staggered(self._field)
            neighbor = self._field.staggered_stencil[index]
            neighbor = direction_string_to_offset(neighbor, self._field.spatial_dimensions)
787
            return [(o - sp.Rational(int(neighbor[i]), 2)) for i, o in enumerate(offsets)]
788

Martin Bauer's avatar
Martin Bauer committed
789
        def _latex(self, _):
790
            n = self._field.latex_name if self._field.latex_name else self._field.name
Martin Bauer's avatar
Martin Bauer committed
791
            offset_str = ",".join([sp.latex(o) for o in self.offsets])
792
            if FieldType.is_staggered(self._field):
793
794
                offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
                                       for i in range(len(self.offsets))])
Martin Bauer's avatar
Martin Bauer committed
795
796
797
798
799
            if self.is_absolute_access:
                offset_str = "\\mathbf{}".format(offset_str)
            elif self.field.spatial_dimensions > 1:
                offset_str = "({})".format(offset_str)

800
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
801
802
803
804
805
                if self.index and self.field.index_dimensions > 1:
                    return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index[1:]
                                                 if len(self.index) > 2 else self.index[1])
                else:
                    return "{{%s}_{%s}}" % (n, offset_str)
Martin Bauer's avatar
Martin Bauer committed
806
            else:
Michael Kuron's avatar
Michael Kuron committed
807
808
809
810
                if self.index and self.field.index_dimensions > 0:
                    return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
                else:
                    return "{{%s}_{%s}}" % (n, offset_str)
Martin Bauer's avatar
Martin Bauer committed
811

812
813
814
        def __str__(self):
            n = self._field.latex_name if self._field.latex_name else self._field.name
            offset_str = ",".join([sp.latex(o) for o in self.offsets])
815
            if FieldType.is_staggered(self._field):
816
817
                offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
                                       for i in range(len(self.offsets))])
818
819
            if self.is_absolute_access:
                offset_str = "[abs]{}".format(offset_str)
Michael Kuron's avatar
Michael Kuron committed
820

821
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
822
823
824
825
                if self.index and self.field.index_dimensions > 1:
                    return "%s[%s](%s)" % (n, offset_str, self.index[1:] if len(self.index) > 2 else self.index[1])
                else:
                    return "%s[%s]" % (n, offset_str)
826
            else:
Michael Kuron's avatar
Michael Kuron committed
827
828
829
830
                if self.index and self.field.index_dimensions > 0:
                    return "%s[%s](%s)" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
                else:
                    return "%s[%s]" % (n, offset_str)
831

Martin Bauer's avatar
Martin Bauer committed
832

Martin Bauer's avatar
Martin Bauer committed
833
834
def get_layout_from_strides(strides: Sequence[int], index_dimension_ids: Optional[List[int]] = None):
    index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
835
    coordinates = list(range(len(strides)))
Martin Bauer's avatar
Martin Bauer committed
836
    relevant_strides = [stride for i, stride in enumerate(strides) if i not in index_dimension_ids]
837
    result = [x for (y, x) in sorted(zip(relevant_strides, coordinates), key=lambda pair: pair[0], reverse=True)]
Martin Bauer's avatar
Martin Bauer committed
838
    return normalize_layout(result)
839
840


Martin Bauer's avatar
Martin Bauer committed
841
842
843
844
845
846
def get_layout_of_array(arr: np.ndarray, index_dimension_ids: Optional[List[int]] = None):
    """ Returns a list indicating the memory layout (linearization order) of the numpy array.

    Examples:
        >>> get_layout_of_array(np.zeros([3,3,3]))
        (0, 1, 2)
Martin Bauer's avatar
Martin Bauer committed
847
848
849
850
851

    In this example the loop over the zeroth coordinate should be the outermost loop,
    followed by the first and second. Elements arr[x,y,0] and arr[x,y,1] are adjacent in memory.
    Normally constructed numpy arrays have this order, however by stride tricks or other frameworks, arrays
    with different memory layout can be created.
Martin Bauer's avatar
Martin Bauer committed
852

Martin Bauer's avatar
Martin Bauer committed
853
    The index_dimension_ids parameter leaves specifies which coordinates should not be
Martin Bauer's avatar
Martin Bauer committed
854
    """
Martin Bauer's avatar
Martin Bauer committed
855
856
    index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
    return get_layout_from_strides(arr.strides, index_dimension_ids)
857
858


Martin Bauer's avatar
Martin Bauer committed
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
def create_numpy_array_with_layout(shape, layout, alignment=False, byte_offset=0, **kwargs):
    """Creates numpy array with given memory layout.

    Args:
        shape: shape of the resulting array
        layout: layout as tuple, where the coordinates are ordered from slow to fast
        alignment: number of bytes to align the beginning and the innermost coordinate to, or False for no alignment
        byte_offset: only used when alignment is specified, align not beginning but address at this offset
                     mostly used to align first inner cell, not ghost cells

    Example:
        >>> res = create_numpy_array_with_layout(shape=(2, 3, 4, 5), layout=(3, 2, 0, 1))
        >>> res.shape
        (2, 3, 4, 5)
        >>> get_layout_of_array(res)
        (3, 2, 0, 1)
875
876
    """
    assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
Martin Bauer's avatar
Martin Bauer committed
877
    cur_layout = list(range(len(shape)))
878
879
    swaps = []
    for i in range(len(layout)):
Martin Bauer's avatar
Martin Bauer committed
880
881
882
883
884
        if cur_layout[i] != layout[i]:
            index_to_swap_with = cur_layout.index(layout[i])
            swaps.append((i, index_to_swap_with))
            cur_layout[i], cur_layout[index_to_swap_with] = cur_layout[index_to_swap_with], cur_layout[i]
    assert tuple(cur_layout) == tuple(layout)
885
886
887
888
889

    shape = list(shape)
    for a, b in swaps:
        shape[a], shape[b] = shape[b], shape[a]

890
891
892
893
894
    if not alignment:
        res = np.empty(shape, order='c', **kwargs)
    else:
        if alignment is True:
            alignment = 8 * 4
Martin Bauer's avatar
Martin Bauer committed
895
        res = aligned_empty(shape, alignment, byte_offset=byte_offset, **kwargs)
896

897
898
899
900
901
    for a, b in reversed(swaps):
        res = res.swapaxes(a, b)
    return res


Martin Bauer's avatar
Martin Bauer committed
902
903
def spatial_layout_string_to_tuple(layout_str: str, dim: int) -> Tuple[int, ...]:
    if layout_str in ('fzyx', 'zyxf'):
904
905
        assert dim <= 3
        return tuple(reversed(range(dim)))
906

Martin Bauer's avatar
Martin Bauer committed
907
    if layout_str in ('fzyx', 'f', 'reverse_numpy', 'SoA'):
908
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
909
    elif layout_str in ('c', 'numpy', 'AoS'):
910
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
911
    raise ValueError("Unknown layout descriptor " + layout_str)
912
913


Martin Bauer's avatar
Martin Bauer committed
914
915
916
def layout_string_to_tuple(layout_str, dim):
    layout_str = layout_str.lower()
    if layout_str == 'fzyx' or layout_str == 'soa':
917
918
        assert dim <= 4
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
919
    elif layout_str == 'zyxf' or layout_str == 'aos':
920
        assert dim <= 4
Martin Bauer's avatar
Martin Bauer committed
921
        return tuple(reversed(range(dim - 1))) + (dim - 1,)
Martin Bauer's avatar
Martin Bauer committed
922
    elif layout_str == 'f' or layout_str == 'reverse_numpy':
923
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
924
    elif layout_str == 'c' or layout_str == 'numpy':
925
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
926
    raise ValueError("Unknown layout descriptor " + layout_str)
927
928


Martin Bauer's avatar
Martin Bauer committed
929
def normalize_layout(layout):
930
    """Takes a layout tuple and subtracts the minimum from all entries"""
Martin Bauer's avatar
Martin Bauer committed
931
932
    min_entry = min(layout)
    return tuple(i - min_entry for i in layout)
933
934


Martin Bauer's avatar
Martin Bauer committed
935
def compute_strides(shape, layout):
936
937
    """
    Computes strides assuming no padding exists
Martin Bauer's avatar
Martin Bauer committed
938
939
940
941
942
943
944

    Args:
        shape: shape (size) of array
        layout: layout specification as tuple

    Returns:
        strides in elements, not in bytes
945
    """
Martin Bauer's avatar
Martin Bauer committed
946
947
948
949
    dim = len(shape)
    assert len(layout) == dim
    assert len(set(layout)) == dim
    strides = [0] * dim
950
    product = 1
951
    for j in reversed(layout):
952
953
954
        strides[j] = product
        product *= shape[j]
    return tuple(strides)
Martin Bauer's avatar
Martin Bauer committed
955
956


957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
# ---------------------------------------- Parsing of string in fields() function --------------------------------------

field_description_regex = re.compile(r"""
    \s*                 # ignore leading white spaces
    (\w+)               # identifier is a sequence of alphanumeric characters, is stored in first group
    (?:                 # optional index specification e.g. (1, 4, 2)
        \s*
        \(
            ([^\)]+)    # read everything up to closing bracket
        \)
        \s*
    )?
    \s*,?\s*             # ignore trailing white spaces and comma
""", re.VERBOSE)

type_description_regex = re.compile(r"""
    \s*
    (\w+)?       # optional dtype
    \s*
    \[
        ([^\]]+)
    \]
    \s*
""", re.VERBOSE | re.IGNORECASE)
981
982
983


def _parse_description(description):
984
985
986
    def parse_part1(d):
        result = field_description_regex.match(d)
        while result:
987
            name, index_str = result.group(1), result.group(2)
988
989
990
991
992
993
994
995
            index = tuple(int(e) for e in index_str.split(",")) if index_str else ()
            yield name, index
            d = d[result.end():]
            result = field_description_regex.match(d)

    def parse_part2(d):
        result = type_description_regex.match(d)
        if result:
996
            data_type_str, size_info = result.group(1), result.group(2).strip().lower()
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
            if data_type_str is None:
                data_type_str = 'float64'
            data_type_str = data_type_str.lower().strip()

            if not data_type_str:
                data_type_str = 'float64'
            if size_info.endswith('d'):
                size_info = int(size_info[:-1])
            else:
                size_info = tuple(int(e) for e in size_info.split(","))
            return data_type_str, size_info
        else:
            raise ValueError("Could not parse field description")

1011
    if ':' in description:
1012
        field_description, field_info = description.split(':')
1013
    else:
1014
1015
1016
1017
1018
        field_description, field_info = description, 'float64[2D]'

    fields_info = [e for e in parse_part1(field_description)]
    if not field_info:
        raise ValueError("Could not parse field description")
1019

1020
1021
    data_type, size = parse_part2(field_info)
    return fields_info, data_type, size