field.py 31.9 KB
Newer Older
1
from enum import Enum
2
from itertools import chain
Martin Bauer's avatar
Martin Bauer committed
3
from typing import Tuple, Sequence, Optional, List, Set
4
5
import numpy as np
import sympy as sp
6
import re
7
from sympy.core.cache import cacheit
8
from pystencils.alignedarray import aligned_empty
Martin Bauer's avatar
Martin Bauer committed
9
from pystencils.data_types import create_type, StructType
10
from pystencils.kernelparameters import FieldShapeSymbol, FieldStrideSymbol
11
from pystencils.stencils import offset_to_direction_string, direction_string_to_offset
Martin Bauer's avatar
Martin Bauer committed
12
from pystencils.sympyextensions import is_integer_sequence
13

Martin Bauer's avatar
Martin Bauer committed
14
15
__all__ = ['Field', 'fields', 'FieldType']

16

17
18
19
20
def fields(description=None, index_dimensions=0, layout=None, **kwargs):
    """Creates pystencils fields from a string description.

    Examples:
Martin Bauer's avatar
Martin Bauer committed
21
22
23
24
        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,))
25

Martin Bauer's avatar
Martin Bauer committed
26
27
28
29
        Create an integer field of shape (10, 20):
            >>> f = fields("f : int32[10, 20]")
            >>> f.has_fixed_shape, f.shape
            (True, (10, 20))
30

Martin Bauer's avatar
Martin Bauer committed
31
32
33
34
35
        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,)
36
37


Martin Bauer's avatar
Martin Bauer committed
38
39
40
41
42
43
44
45
46
47
        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)
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
    """
    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
                f = Field.create_from_numpy_array(field_name, kwargs[field_name], index_dimensions=len(idx_shape))
            elif isinstance(shape, tuple):
                f = Field.create_fixed_size(field_name, shape + idx_shape, dtype=dtype,
                                            index_dimensions=len(idx_shape), layout=layout)
            elif isinstance(shape, int):
                f = Field.create_generic(field_name, spatial_dimensions=shape, dtype=dtype,
                                         index_shape=idx_shape, layout=layout)
            elif shape is None:
                f = Field.create_generic(field_name, spatial_dimensions=2, dtype=dtype,
                                         index_shape=idx_shape, layout=layout)
            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():
            result.append(Field.create_from_numpy_array(field_name, arr, index_dimensions=index_dimensions))

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


84
85
86
87
88
89
90
91
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
Martin Bauer's avatar
Martin Bauer committed
92
93
94
    # 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
95
96

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
97
    def is_generic(field):
98
        assert isinstance(field, Field)
Martin Bauer's avatar
Martin Bauer committed
99
        return field.field_type == FieldType.GENERIC
100
101

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
102
    def is_indexed(field):
103
        assert isinstance(field, Field)
Martin Bauer's avatar
Martin Bauer committed
104
        return field.field_type == FieldType.INDEXED
105
106

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
107
    def is_buffer(field):
108
        assert isinstance(field, Field)
Martin Bauer's avatar
Martin Bauer committed
109
        return field.field_type == FieldType.BUFFER
110

Martin Bauer's avatar
Martin Bauer committed
111
112
113
114
115
    @staticmethod
    def is_custom(field):
        assert isinstance(field, Field)
        return field.field_type == FieldType.CUSTOM

116

117
class Field:
118
119
120
121
    """
    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
122
    Creating Fields:
Martin Bauer's avatar
Martin Bauer committed
123
124
        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`
125
        and `Field.create_fixed_size`. Don't instantiate the Field directly!
Martin Bauer's avatar
Martin Bauer committed
126
127
128
129
130
        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`
131
        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
132
           beforehand for a library. (see `Field.create_generic`)
133

Martin Bauer's avatar
Martin Bauer committed
134
    Dimensions and Indexing:
135
136
        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
137
        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
138
        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
139
        are four dimensions, two spatial and two index dimensions: ``len(arr.shape) == spatial_dims + index_dims``
140

Martin Bauer's avatar
Martin Bauer committed
141
142
143
144
145
        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
146
        First specify the spatial offsets in [], then in case index_dimension>0 the indices in ()
Martin Bauer's avatar
Martin Bauer committed
147
        e.g. ``f[-1,0,0](7)``
148

Martin Bauer's avatar
Martin Bauer committed
149
    Example using no index dimensions:
150
        >>> a = np.zeros([10, 10])
Martin Bauer's avatar
Martin Bauer committed
151
        >>> f = Field.create_from_numpy_array("f", a, index_dimensions=0)
Martin Bauer's avatar
Martin Bauer committed
152
        >>> jacobi = (f[-1,0] + f[1,0] + f[0,-1] + f[0,1]) / 4
153

Martin Bauer's avatar
Martin Bauer committed
154
    Examples for index dimensions to create LB field and implement stream pull:
Martin Bauer's avatar
Martin Bauer committed
155
        >>> from pystencils import Assignment
156
        >>> stencil = np.array([[0,0], [0,1], [0,-1]])
Martin Bauer's avatar
Martin Bauer committed
157
        >>> src, dst = fields("src(3), dst(3) : double[2D]")
158
        >>> assignments = [Assignment(dst[0,0](i), src[-offset](i)) for i, offset in enumerate(stencil)];
159
    """
160
161

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
162
163
    def create_generic(field_name, spatial_dimensions, dtype=np.float64, index_dimensions=0, layout='numpy',
                       index_shape=None, field_type=FieldType.GENERIC) -> 'Field':
164
165
166
        """
        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
167
168
169
170
171
172
173
        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
174
                    over dimension 0. Also allowed: the strings 'numpy' (0,1,..d) or 'reverse_numpy' (d, ..., 1, 0)
Martin Bauer's avatar
Martin Bauer committed
175
176
177
178
179
            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
                        that should be iterated over, and BUFFER fields that are used to generate
                        communication packing/unpacking kernels
180
        """
181
182
183
        if index_shape is not None:
            assert index_dimensions == 0 or index_dimensions == len(index_shape)
            index_dimensions = len(index_shape)
184
        if isinstance(layout, str):
Martin Bauer's avatar
Martin Bauer committed
185
            layout = spatial_layout_string_to_tuple(layout, dim=spatial_dimensions)
186

Martin Bauer's avatar
Martin Bauer committed
187
188
        total_dimensions = spatial_dimensions + index_dimensions
        if index_shape is None or len(index_shape) == 0:
189
            shape = tuple([FieldShapeSymbol([field_name], i) for i in range(total_dimensions)])
190
        else:
191
            shape = tuple([FieldShapeSymbol([field_name], i) for i in range(spatial_dimensions)] + list(index_shape))
192

193
        strides = tuple([FieldStrideSymbol(field_name, i) for i in range(total_dimensions)])
194

Martin Bauer's avatar
Martin Bauer committed
195
196
197
        np_data_type = np.dtype(dtype)
        if np_data_type.fields is not None:
            if index_dimensions != 0:
198
199
200
201
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

Martin Bauer's avatar
Martin Bauer committed
202
        return Field(field_name, field_type, dtype, layout, shape, strides)
203

204
    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
205
206
207
    def create_from_numpy_array(field_name: str, array: np.ndarray, index_dimensions: int = 0) -> 'Field':
        """Creates a field based on the layout, data type, and shape of a given numpy array.

208
        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
209
210
211
212
213

        Args:
            field_name: symbolic name for the field
            array: numpy array
            index_dimensions: see documentation of Field
214
        """
Martin Bauer's avatar
Martin Bauer committed
215
216
        spatial_dimensions = len(array.shape) - index_dimensions
        if spatial_dimensions < 1:
217
218
            raise ValueError("Too many index dimensions. At least one spatial dimension required")

Martin Bauer's avatar
Martin Bauer committed
219
220
221
        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
222

Martin Bauer's avatar
Martin Bauer committed
223
224
        strides = tuple([s // np.dtype(array.dtype).itemsize for s in array.strides])
        shape = tuple(int(s) for s in array.shape)
225

Martin Bauer's avatar
Martin Bauer committed
226
227
228
        numpy_dtype = np.dtype(array.dtype)
        if numpy_dtype.fields is not None:
            if index_dimensions != 0:
229
230
231
232
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

Martin Bauer's avatar
Martin Bauer committed
233
        return Field(field_name, FieldType.GENERIC, array.dtype, spatial_layout, shape, strides)
234
235

    @staticmethod
Martin Bauer's avatar
Martin Bauer committed
236
    def create_fixed_size(field_name: str, shape: Tuple[int, ...], index_dimensions: int = 0,
237
                          dtype=np.float64, layout: str = 'numpy', strides: Optional[Sequence[int]] = None) -> 'Field':
238
        """
239
        Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout
240

Martin Bauer's avatar
Martin Bauer committed
241
242
243
244
245
246
247
        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)
248
        """
Martin Bauer's avatar
Martin Bauer committed
249
250
        spatial_dimensions = len(shape) - index_dimensions
        assert spatial_dimensions >= 1
251

252
        if isinstance(layout, str):
Martin Bauer's avatar
Martin Bauer committed
253
            layout = layout_string_to_tuple(layout, spatial_dimensions + index_dimensions)
254
255

        shape = tuple(int(s) for s in shape)
256
        if strides is None:
Martin Bauer's avatar
Martin Bauer committed
257
            strides = compute_strides(shape, layout)
258
259
260
        else:
            assert len(strides) == len(shape)
            strides = tuple([s // np.dtype(dtype).itemsize for s in strides])
261

Martin Bauer's avatar
Martin Bauer committed
262
263
264
        numpy_dtype = np.dtype(dtype)
        if numpy_dtype.fields is not None:
            if index_dimensions != 0:
265
266
267
268
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

Martin Bauer's avatar
Martin Bauer committed
269
270
271
272
        spatial_layout = list(layout)
        for i in range(spatial_dimensions, len(layout)):
            spatial_layout.remove(i)
        return Field(field_name, FieldType.GENERIC, dtype, tuple(spatial_layout), shape, strides)
273

Martin Bauer's avatar
Martin Bauer committed
274
    def __init__(self, field_name, field_type, dtype, layout, shape, strides):
275
        """Do not use directly. Use static create* methods"""
276
        self._field_name = field_name
Martin Bauer's avatar
Martin Bauer committed
277
        assert isinstance(field_type, FieldType)
278
        assert len(shape) == len(strides)
Martin Bauer's avatar
Martin Bauer committed
279
        self.field_type = field_type
Martin Bauer's avatar
Martin Bauer committed
280
        self._dtype = create_type(dtype)
Martin Bauer's avatar
Martin Bauer committed
281
        self._layout = normalize_layout(layout)
282
283
        self.shape = shape
        self.strides = strides
284
        self.latex_name = None  # type: Optional[str]
285

Martin Bauer's avatar
Martin Bauer committed
286
    def new_field_with_different_name(self, new_name):
Martin Bauer's avatar
Martin Bauer committed
287
        return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
288

289
    @property
Martin Bauer's avatar
Martin Bauer committed
290
    def spatial_dimensions(self) -> int:
291
292
293
        return len(self._layout)

    @property
Martin Bauer's avatar
Martin Bauer committed
294
    def index_dimensions(self) -> int:
295
        return len(self.shape) - len(self._layout)
296
297
298
299
300
301

    @property
    def layout(self):
        return self._layout

    @property
Martin Bauer's avatar
Martin Bauer committed
302
    def name(self) -> str:
303
        return self._field_name
304
305

    @property
Martin Bauer's avatar
Martin Bauer committed
306
307
    def spatial_shape(self) -> Tuple[int, ...]:
        return self.shape[:self.spatial_dimensions]
308

309
    @property
Martin Bauer's avatar
Martin Bauer committed
310
    def has_fixed_shape(self):
Martin Bauer's avatar
Martin Bauer committed
311
        return is_integer_sequence(self.shape)
312

313
    @property
Martin Bauer's avatar
Martin Bauer committed
314
315
    def index_shape(self):
        return self.shape[self.spatial_dimensions:]
316

317
    @property
Martin Bauer's avatar
Martin Bauer committed
318
319
    def has_fixed_index_shape(self):
        return is_integer_sequence(self.index_shape)
320

321
    @property
Martin Bauer's avatar
Martin Bauer committed
322
323
    def spatial_strides(self):
        return self.strides[:self.spatial_dimensions]
324
325

    @property
Martin Bauer's avatar
Martin Bauer committed
326
327
    def index_strides(self):
        return self.strides[self.spatial_dimensions:]
328
329
330
331
332
333

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

    def __repr__(self):
334
        return self._field_name
335

Martin Bauer's avatar
Martin Bauer committed
336
337
338
339
    def neighbor(self, coord_id, offset):
        offset_list = [0] * self.spatial_dimensions
        offset_list[coord_id] = offset
        return Field.Access(self, tuple(offset_list))
340

341
    def neighbors(self, stencil):
342
        return [self.__getitem__(s) for s in stencil]
343

344
    @property
Martin Bauer's avatar
Martin Bauer committed
345
346
347
    def center_vector(self):
        index_shape = self.index_shape
        if len(index_shape) == 0:
348
            return self.center
Martin Bauer's avatar
Martin Bauer committed
349
350
351
        elif len(index_shape) == 1:
            return sp.Matrix([self(i) for i in range(index_shape[0])])
        elif len(index_shape) == 2:
352
353
354
            def cb(*args):
                r = self.__call__(*args)
                return r
Martin Bauer's avatar
Martin Bauer committed
355
            return sp.Matrix(*index_shape, cb)
356

357
    @property
358
    def center(self):
Martin Bauer's avatar
Martin Bauer committed
359
        center = tuple([0] * self.spatial_dimensions)
360
361
        return Field.Access(self, center)

362
363
364
365
    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
366
            offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
367
368
        if type(offset) is not tuple:
            offset = (offset,)
Martin Bauer's avatar
Martin Bauer committed
369
        if len(offset) != self.spatial_dimensions:
370
            raise ValueError("Wrong number of spatial indices: "
Martin Bauer's avatar
Martin Bauer committed
371
                             "Got %d, expected %d" % (len(offset), self.spatial_dimensions))
372
373
        return Field.Access(self, offset)

Martin Bauer's avatar
Martin Bauer committed
374
    def absolute_access(self, offset, index):
Martin Bauer's avatar
Martin Bauer committed
375
        assert FieldType.is_custom(self)
Martin Bauer's avatar
Martin Bauer committed
376
377
        return Field.Access(self, offset, index, is_absolute_access=True)

378
    def __call__(self, *args, **kwargs):
Martin Bauer's avatar
Martin Bauer committed
379
        center = tuple([0] * self.spatial_dimensions)
380
381
        return Field.Access(self, center)(*args, **kwargs)

382
    def hashable_contents(self):
383
384
        dth = hash(self._dtype)
        return self._layout, self.shape, self.strides, dth, self.field_type, self._field_name, self.latex_name
385

386
    def __hash__(self):
387
        return hash(self.hashable_contents())
388
389

    def __eq__(self, other):
390
391
        if not isinstance(other, Field):
            return False
392
        return self.hashable_contents() == other.hashable_contents()
393

Martin Bauer's avatar
Martin Bauer committed
394
    # noinspection PyAttributeOutsideInit,PyUnresolvedReferences
395
    class Access(sp.Symbol):
Martin Bauer's avatar
Martin Bauer committed
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
        """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
        """
414
415
416
417
        def __new__(cls, name, *args, **kwargs):
            obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
            return obj

Martin Bauer's avatar
Martin Bauer committed
418
        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False):
Martin Bauer's avatar
Martin Bauer committed
419
420
421
            field_name = field.name
            offsets_and_index = chain(offsets, idx) if idx is not None else offsets
            constant_offsets = not any([isinstance(o, sp.Basic) and not o.is_Integer for o in offsets_and_index])
422
423

            if not idx:
Martin Bauer's avatar
Martin Bauer committed
424
                idx = tuple([0] * field.index_dimensions)
425

Martin Bauer's avatar
Martin Bauer committed
426
427
428
            if constant_offsets:
                offset_name = offset_to_direction_string(offsets)
                if field.index_dimensions == 0:
429
                    superscript = None
Martin Bauer's avatar
Martin Bauer committed
430
                elif field.index_dimensions == 1:
431
                    superscript = str(idx[0])
432
                else:
Martin Bauer's avatar
Martin Bauer committed
433
434
435
436
                    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):
437
438
                        if i >= bound:
                            raise ValueError("Field index out of bounds")
439
            else:
Martin Bauer's avatar
Martin Bauer committed
440
                offset_name = "%0.10X" % (abs(hash(tuple(offsets_and_index))))
441
                superscript = None
442

Martin Bauer's avatar
Martin Bauer committed
443
            symbol_name = "%s_%s" % (field_name, offset_name)
444
            if superscript is not None:
Martin Bauer's avatar
Martin Bauer committed
445
                symbol_name += "^" + superscript
446

Martin Bauer's avatar
Martin Bauer committed
447
            obj = super(Field.Access, self).__xnew__(self, symbol_name)
448
449
450
451
452
453
454
            obj._field = field
            obj._offsets = []
            for o in offsets:
                if isinstance(o, sp.Basic):
                    obj._offsets.append(o)
                else:
                    obj._offsets.append(int(o))
455
            obj._offsets = tuple(obj._offsets)
Martin Bauer's avatar
Martin Bauer committed
456
            obj._offsetName = offset_name
457
            obj._superscript = superscript
458
459
            obj._index = idx

Martin Bauer's avatar
Martin Bauer committed
460
461
462
463
464
465
            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
466
467
            return obj

468
        def __getnewargs__(self):
Martin Bauer's avatar
Martin Bauer committed
469
            return self.field, self.offsets, self.index, self.is_absolute_access
470

Martin Bauer's avatar
Martin Bauer committed
471
        # noinspection SpellCheckingInspection
472
        __xnew__ = staticmethod(__new_stage2__)
Martin Bauer's avatar
Martin Bauer committed
473
        # noinspection SpellCheckingInspection
474
475
476
        __xnew_cached_ = staticmethod(cacheit(__new_stage2__))

        def __call__(self, *idx):
Martin Bauer's avatar
Martin Bauer committed
477
            if self._index != tuple([0] * self.field.index_dimensions):
478
479
480
                raise ValueError("Indexing an already indexed Field.Access")

            idx = tuple(idx)
481

Martin Bauer's avatar
Martin Bauer committed
482
            if self.field.index_dimensions == 0 and idx == (0,):
483
484
                idx = ()

Martin Bauer's avatar
Martin Bauer committed
485
            if len(idx) != self.field.index_dimensions:
486
                raise ValueError("Wrong number of indices: "
Martin Bauer's avatar
Martin Bauer committed
487
                                 "Got %d, expected %d" % (len(idx), self.field.index_dimensions))
488
489
            return Field.Access(self.field, self._offsets, idx)

Martin Bauer's avatar
Martin Bauer committed
490
491
492
        def __getitem__(self, *idx):
            return self.__call__(*idx)

Martin Bauer's avatar
Martin Bauer committed
493
494
495
496
497
        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")

498
        @property
Martin Bauer's avatar
Martin Bauer committed
499
500
        def field(self) -> 'Field':
            """Field that the Access points to"""
501
502
503
            return self._field

        @property
Martin Bauer's avatar
Martin Bauer committed
504
505
        def offsets(self) -> Tuple:
            """Spatial offset as tuple"""
506
            return self._offsets
507

508
        @property
Martin Bauer's avatar
Martin Bauer committed
509
510
        def required_ghost_layers(self) -> int:
            """Largest spatial distance that is accessed."""
511
512
513
            return int(np.max(np.abs(self._offsets)))

        @property
Martin Bauer's avatar
Martin Bauer committed
514
        def nr_of_coordinates(self):
515
516
517
            return len(self._offsets)

        @property
Martin Bauer's avatar
Martin Bauer committed
518
        def offset_name(self) -> str:
Martin Bauer's avatar
Martin Bauer committed
519
520
521
522
523
524
525
            """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'
            """
526
527
528
529
            return self._offsetName

        @property
        def index(self):
Martin Bauer's avatar
Martin Bauer committed
530
            """Value of index coordinates as tuple."""
531
532
            return self._index

Martin Bauer's avatar
Martin Bauer committed
533
        def neighbor(self, coord_id: int, offset: Sequence[int]) -> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
534
535
536
537
538
539
540
541
542
543
544
            """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
545
546
547
            offset_list = list(self.offsets)
            offset_list[coord_id] += offset
            return Field.Access(self.field, tuple(offset_list), self.index)
548

Martin Bauer's avatar
Martin Bauer committed
549
        def get_shifted(self, *shift)-> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
550
551
552
553
554
555
556
            """Returns a new Access with changed spatial coordinates

            Example:
                >>> f = fields("f: [2D]")
                >>> f[0,0].get_shifted(1, 1)
                f_NE
            """
557
558
            return Field.Access(self.field, tuple(a + b for a, b in zip(shift, self.offsets)), self.index)

Martin Bauer's avatar
Martin Bauer committed
559
560
561
562
563
564
565
566
        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
            """
567
568
            return Field.Access(self.field, self.offsets, idx_tuple)

Martin Bauer's avatar
Martin Bauer committed
569
570
571
572
573
574
575
576
577
578
579
580
581
        @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

582
        def _hashable_content(self):
583
584
            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
585

Martin Bauer's avatar
Martin Bauer committed
586
        def _latex(self, _):
587
            n = self._field.latex_name if self._field.latex_name else self._field.name
Martin Bauer's avatar
Martin Bauer committed
588
589
590
591
592
593
594
595
            offset_str = ",".join([sp.latex(o) for o in self.offsets])
            if self.is_absolute_access:
                offset_str = "\\mathbf{}".format(offset_str)
            elif self.field.spatial_dimensions > 1:
                offset_str = "({})".format(offset_str)

            if self.index and self.index != (0,):
                return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
Martin Bauer's avatar
Martin Bauer committed
596
            else:
Martin Bauer's avatar
Martin Bauer committed
597
                return "{{%s}_{%s}}" % (n, offset_str)
Martin Bauer's avatar
Martin Bauer committed
598

599
600
601
602
603
604
605
606
607
608
        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])
            if self.is_absolute_access:
                offset_str = "[abs]{}".format(offset_str)
            if self.index and self.index != (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
609

Martin Bauer's avatar
Martin Bauer committed
610
611
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
612
    coordinates = list(range(len(strides)))
Martin Bauer's avatar
Martin Bauer committed
613
    relevant_strides = [stride for i, stride in enumerate(strides) if i not in index_dimension_ids]
614
    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
615
    return normalize_layout(result)
616
617


Martin Bauer's avatar
Martin Bauer committed
618
619
620
621
622
623
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
624
625
626
627
628

    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
629

Martin Bauer's avatar
Martin Bauer committed
630
    The index_dimension_ids parameter leaves specifies which coordinates should not be
Martin Bauer's avatar
Martin Bauer committed
631
    """
Martin Bauer's avatar
Martin Bauer committed
632
633
    index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
    return get_layout_from_strides(arr.strides, index_dimension_ids)
634
635


Martin Bauer's avatar
Martin Bauer committed
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
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)
652
653
    """
    assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
Martin Bauer's avatar
Martin Bauer committed
654
    cur_layout = list(range(len(shape)))
655
656
    swaps = []
    for i in range(len(layout)):
Martin Bauer's avatar
Martin Bauer committed
657
658
659
660
661
        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)
662
663
664
665
666

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

667
668
669
670
671
    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
672
        res = aligned_empty(shape, alignment, byte_offset=byte_offset, **kwargs)
673

674
675
676
677
678
    for a, b in reversed(swaps):
        res = res.swapaxes(a, b)
    return res


Martin Bauer's avatar
Martin Bauer committed
679
680
def spatial_layout_string_to_tuple(layout_str: str, dim: int) -> Tuple[int, ...]:
    if layout_str in ('fzyx', 'zyxf'):
681
682
        assert dim <= 3
        return tuple(reversed(range(dim)))
683

Martin Bauer's avatar
Martin Bauer committed
684
    if layout_str in ('fzyx', 'f', 'reverse_numpy', 'SoA'):
685
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
686
    elif layout_str in ('c', 'numpy', 'AoS'):
687
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
688
    raise ValueError("Unknown layout descriptor " + layout_str)
689
690


Martin Bauer's avatar
Martin Bauer committed
691
692
693
def layout_string_to_tuple(layout_str, dim):
    layout_str = layout_str.lower()
    if layout_str == 'fzyx' or layout_str == 'soa':
694
695
        assert dim <= 4
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
696
    elif layout_str == 'zyxf' or layout_str == 'aos':
697
        assert dim <= 4
Martin Bauer's avatar
Martin Bauer committed
698
        return tuple(reversed(range(dim - 1))) + (dim - 1,)
Martin Bauer's avatar
Martin Bauer committed
699
    elif layout_str == 'f' or layout_str == 'reverse_numpy':
700
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
701
    elif layout_str == 'c' or layout_str == 'numpy':
702
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
703
    raise ValueError("Unknown layout descriptor " + layout_str)
704
705


Martin Bauer's avatar
Martin Bauer committed
706
def normalize_layout(layout):
707
    """Takes a layout tuple and subtracts the minimum from all entries"""
Martin Bauer's avatar
Martin Bauer committed
708
709
    min_entry = min(layout)
    return tuple(i - min_entry for i in layout)
710
711


Martin Bauer's avatar
Martin Bauer committed
712
def compute_strides(shape, layout):
713
714
    """
    Computes strides assuming no padding exists
Martin Bauer's avatar
Martin Bauer committed
715
716
717
718
719
720
721

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

    Returns:
        strides in elements, not in bytes
722
    """
Martin Bauer's avatar
Martin Bauer committed
723
724
725
726
    dim = len(shape)
    assert len(layout) == dim
    assert len(set(layout)) == dim
    strides = [0] * dim
727
    product = 1
728
    for j in reversed(layout):
729
730
731
        strides[j] = product
        product *= shape[j]
    return tuple(strides)
Martin Bauer's avatar
Martin Bauer committed
732
733


734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
# ---------------------------------------- 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)
758
759
760


def _parse_description(description):
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
    def parse_part1(d):
        result = field_description_regex.match(d)
        while result:
            name, index_str = result[1], result[2]
            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:
            data_type_str, size_info = result[1], result[2].strip().lower()
            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")

788
    if ':' in description:
789
        field_description, field_info = description.split(':')
790
    else:
791
792
793
794
795
        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")
796

797
798
    data_type, size = parse_part2(field_info)
    return fields_info, data_type, size