field.py 40.7 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

Martin Bauer's avatar
Martin Bauer committed
330
    def new_field_with_different_name(self, new_name):
331
332
333
334
335
        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)
336

337
    @property
Martin Bauer's avatar
Martin Bauer committed
338
    def spatial_dimensions(self) -> int:
339
340
341
        return len(self._layout)

    @property
Martin Bauer's avatar
Martin Bauer committed
342
    def index_dimensions(self) -> int:
343
        return len(self.shape) - len(self._layout)
344

345
346
347
348
    @property
    def ndim(self) -> int:
        return len(self.shape)

349
350
351
    def values_per_cell(self) -> int:
        return functools.reduce(operator.mul, self.index_shape, 1)

352
353
354
355
356
    @property
    def layout(self):
        return self._layout

    @property
Martin Bauer's avatar
Martin Bauer committed
357
    def name(self) -> str:
358
        return self._field_name
359
360

    @property
Martin Bauer's avatar
Martin Bauer committed
361
362
    def spatial_shape(self) -> Tuple[int, ...]:
        return self.shape[:self.spatial_dimensions]
363

364
    @property
Martin Bauer's avatar
Martin Bauer committed
365
    def has_fixed_shape(self):
Martin Bauer's avatar
Martin Bauer committed
366
        return is_integer_sequence(self.shape)
367

368
    @property
Martin Bauer's avatar
Martin Bauer committed
369
370
    def index_shape(self):
        return self.shape[self.spatial_dimensions:]
371

372
    @property
Martin Bauer's avatar
Martin Bauer committed
373
374
    def has_fixed_index_shape(self):
        return is_integer_sequence(self.index_shape)
375

376
    @property
Martin Bauer's avatar
Martin Bauer committed
377
378
    def spatial_strides(self):
        return self.strides[:self.spatial_dimensions]
379
380

    @property
Martin Bauer's avatar
Martin Bauer committed
381
382
    def index_strides(self):
        return self.strides[self.spatial_dimensions:]
383
384
385
386
387

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

388
389
390
391
    @property
    def itemsize(self):
        return self.dtype.numpy_dtype.itemsize

392
    def __repr__(self):
393
        return self._field_name
394

Martin Bauer's avatar
Martin Bauer committed
395
396
397
398
    def neighbor(self, coord_id, offset):
        offset_list = [0] * self.spatial_dimensions
        offset_list[coord_id] = offset
        return Field.Access(self, tuple(offset_list))
399

400
    def neighbors(self, stencil):
401
        return [self.__getitem__(s) for s in stencil]
402

403
    @property
Martin Bauer's avatar
Martin Bauer committed
404
405
406
    def center_vector(self):
        index_shape = self.index_shape
        if len(index_shape) == 0:
407
408
            return sp.Matrix([self.center])
        if len(index_shape) == 1:
Martin Bauer's avatar
Martin Bauer committed
409
410
            return sp.Matrix([self(i) for i in range(index_shape[0])])
        elif len(index_shape) == 2:
411
412
413
            def cb(*args):
                r = self.__call__(*args)
                return r
Martin Bauer's avatar
Martin Bauer committed
414
            return sp.Matrix(*index_shape, cb)
415

416
    @property
417
    def center(self):
Martin Bauer's avatar
Martin Bauer committed
418
        center = tuple([0] * self.spatial_dimensions)
419
420
        return Field.Access(self, center)

421
422
423
424
    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
425
            offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
426
427
        if type(offset) is not tuple:
            offset = (offset,)
Martin Bauer's avatar
Martin Bauer committed
428
        if len(offset) != self.spatial_dimensions:
429
            raise ValueError("Wrong number of spatial indices: "
Martin Bauer's avatar
Martin Bauer committed
430
                             "Got %d, expected %d" % (len(offset), self.spatial_dimensions))
431
432
        return Field.Access(self, offset)

Martin Bauer's avatar
Martin Bauer committed
433
    def absolute_access(self, offset, index):
Martin Bauer's avatar
Martin Bauer committed
434
        assert FieldType.is_custom(self)
Martin Bauer's avatar
Martin Bauer committed
435
436
        return Field.Access(self, offset, index, is_absolute_access=True)

437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
    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
458
459
460
461
462
463
464
    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.
        """
465
        assert FieldType.is_staggered(self)
Michael Kuron's avatar
Michael Kuron committed
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502

        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)
        for i, o in enumerate(offset):
            if (o + sp.Rational(1, 2)).is_Integer:
                offset[i] += sp.Rational(1, 2)
                idx = i
        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))

503
    def __call__(self, *args, **kwargs):
Martin Bauer's avatar
Martin Bauer committed
504
        center = tuple([0] * self.spatial_dimensions)
505
506
        return Field.Access(self, center)(*args, **kwargs)

507
    def hashable_contents(self):
508
509
        dth = hash(self._dtype)
        return self._layout, self.shape, self.strides, dth, self.field_type, self._field_name, self.latex_name
510

511
    def __hash__(self):
512
        return hash(self.hashable_contents())
513
514

    def __eq__(self, other):
515
516
        if not isinstance(other, Field):
            return False
517
        return self.hashable_contents() == other.hashable_contents()
518

519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
    @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
547
    # noinspection PyAttributeOutsideInit,PyUnresolvedReferences
548
    class Access(TypedSymbol, AbstractField.AbstractAccess):
Martin Bauer's avatar
Martin Bauer committed
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
        """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
        """
567

568
569
570
571
        def __new__(cls, name, *args, **kwargs):
            obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
            return obj

572
        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False, dtype=None):
Martin Bauer's avatar
Martin Bauer committed
573
            field_name = field.name
Martin Bauer's avatar
Martin Bauer committed
574
            offsets_and_index = (*offsets, *idx) if idx is not None else offsets
Martin Bauer's avatar
Martin Bauer committed
575
            constant_offsets = not any([isinstance(o, sp.Basic) and not o.is_Integer for o in offsets_and_index])
576
577

            if not idx:
Martin Bauer's avatar
Martin Bauer committed
578
                idx = tuple([0] * field.index_dimensions)
579

Martin Bauer's avatar
Martin Bauer committed
580
581
582
            if constant_offsets:
                offset_name = offset_to_direction_string(offsets)
                if field.index_dimensions == 0:
583
                    superscript = None
Martin Bauer's avatar
Martin Bauer committed
584
                elif field.index_dimensions == 1:
585
                    superscript = str(idx[0])
586
                else:
Martin Bauer's avatar
Martin Bauer committed
587
588
589
590
                    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):
591
592
                        if i >= bound:
                            raise ValueError("Field index out of bounds")
593
            else:
594
                offset_name = hashlib.md5(pickle.dumps(offsets_and_index)).hexdigest()[:12]
595
                superscript = None
596

Martin Bauer's avatar
Martin Bauer committed
597
            symbol_name = "%s_%s" % (field_name, offset_name)
598
            if superscript is not None:
Martin Bauer's avatar
Martin Bauer committed
599
                symbol_name += "^" + superscript
600

601
            obj = super(Field.Access, self).__xnew__(self, symbol_name, field.dtype)
602
603
604
605
606
607
608
            obj._field = field
            obj._offsets = []
            for o in offsets:
                if isinstance(o, sp.Basic):
                    obj._offsets.append(o)
                else:
                    obj._offsets.append(int(o))
609
            obj._offsets = tuple(obj._offsets)
Martin Bauer's avatar
Martin Bauer committed
610
            obj._offsetName = offset_name
611
            obj._superscript = superscript
612
613
            obj._index = idx

Martin Bauer's avatar
Martin Bauer committed
614
615
616
617
618
619
            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
620
621
            return obj

622
        def __getnewargs__(self):
623
            return self.field, self.offsets, self.index, self.is_absolute_access, self.dtype
624

Martin Bauer's avatar
Martin Bauer committed
625
        # noinspection SpellCheckingInspection
626
        __xnew__ = staticmethod(__new_stage2__)
Martin Bauer's avatar
Martin Bauer committed
627
        # noinspection SpellCheckingInspection
628
629
630
        __xnew_cached_ = staticmethod(cacheit(__new_stage2__))

        def __call__(self, *idx):
Martin Bauer's avatar
Martin Bauer committed
631
            if self._index != tuple([0] * self.field.index_dimensions):
632
633
634
                raise ValueError("Indexing an already indexed Field.Access")

            idx = tuple(idx)
635

Martin Bauer's avatar
Martin Bauer committed
636
            if self.field.index_dimensions == 0 and idx == (0,):
637
638
                idx = ()

Martin Bauer's avatar
Martin Bauer committed
639
            if len(idx) != self.field.index_dimensions:
640
                raise ValueError("Wrong number of indices: "
Martin Bauer's avatar
Martin Bauer committed
641
                                 "Got %d, expected %d" % (len(idx), self.field.index_dimensions))
642
            return Field.Access(self.field, self._offsets, idx, dtype=self.dtype)
643

Martin Bauer's avatar
Martin Bauer committed
644
645
646
        def __getitem__(self, *idx):
            return self.__call__(*idx)

Martin Bauer's avatar
Martin Bauer committed
647
648
649
650
651
        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")

652
        @property
Martin Bauer's avatar
Martin Bauer committed
653
654
        def field(self) -> 'Field':
            """Field that the Access points to"""
655
656
657
            return self._field

        @property
Martin Bauer's avatar
Martin Bauer committed
658
659
        def offsets(self) -> Tuple:
            """Spatial offset as tuple"""
660
            return self._offsets
661

662
        @property
Martin Bauer's avatar
Martin Bauer committed
663
664
        def required_ghost_layers(self) -> int:
            """Largest spatial distance that is accessed."""
665
666
667
            return int(np.max(np.abs(self._offsets)))

        @property
Martin Bauer's avatar
Martin Bauer committed
668
        def nr_of_coordinates(self):
669
670
671
            return len(self._offsets)

        @property
Martin Bauer's avatar
Martin Bauer committed
672
        def offset_name(self) -> str:
Martin Bauer's avatar
Martin Bauer committed
673
674
675
676
677
678
679
            """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'
            """
680
681
682
683
            return self._offsetName

        @property
        def index(self):
Martin Bauer's avatar
Martin Bauer committed
684
            """Value of index coordinates as tuple."""
685
686
            return self._index

687
        def neighbor(self, coord_id: int, offset: int) -> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
688
689
690
691
692
693
694
695
696
697
698
            """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
699
700
            offset_list = list(self.offsets)
            offset_list[coord_id] += offset
701
            return Field.Access(self.field, tuple(offset_list), self.index, dtype=self.dtype)
702

703
        def get_shifted(self, *shift) -> 'Field.Access':
Martin Bauer's avatar
Martin Bauer committed
704
705
706
707
708
709
710
            """Returns a new Access with changed spatial coordinates

            Example:
                >>> f = fields("f: [2D]")
                >>> f[0,0].get_shifted(1, 1)
                f_NE
            """
711
712
713
714
            return Field.Access(self.field,
                                tuple(a + b for a, b in zip(shift, self.offsets)),
                                self.index,
                                dtype=self.dtype)
715

Martin Bauer's avatar
Martin Bauer committed
716
717
718
719
720
721
722
723
        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
            """
724
            return Field.Access(self.field, self.offsets, idx_tuple, dtype=self.dtype)
725

726
727
728
729
730
731
        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
732
733
734
735
736
737
738
739
740
741
742
743
744
        @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

745
        def _hashable_content(self):
746
747
            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
748

Martin Bauer's avatar
Martin Bauer committed
749
        def _latex(self, _):
750
            n = self._field.latex_name if self._field.latex_name else self._field.name
Martin Bauer's avatar
Martin Bauer committed
751
            offset_str = ",".join([sp.latex(o) for o in self.offsets])
752
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
753
754
                offset_str = ",".join([sp.latex(o - sp.Rational(int(i == self.index[0]), 2))
                                       for i, o in enumerate(self.offsets)])
Martin Bauer's avatar
Martin Bauer committed
755
756
757
758
759
            if self.is_absolute_access:
                offset_str = "\\mathbf{}".format(offset_str)
            elif self.field.spatial_dimensions > 1:
                offset_str = "({})".format(offset_str)

760
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
761
762
763
764
765
                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
766
            else:
Michael Kuron's avatar
Michael Kuron committed
767
768
769
770
                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
771

772
773
774
        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])
775
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
776
777
                offset_str = ",".join([sp.latex(o - sp.Rational(int(i == self.index[0]), 2))
                                       for i, o in enumerate(self.offsets)])
778
779
            if self.is_absolute_access:
                offset_str = "[abs]{}".format(offset_str)
Michael Kuron's avatar
Michael Kuron committed
780

781
            if FieldType.is_staggered(self._field):
Michael Kuron's avatar
Michael Kuron committed
782
783
784
785
                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)
786
            else:
Michael Kuron's avatar
Michael Kuron committed
787
788
789
790
                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)
791

Martin Bauer's avatar
Martin Bauer committed
792

Martin Bauer's avatar
Martin Bauer committed
793
794
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
795
    coordinates = list(range(len(strides)))
Martin Bauer's avatar
Martin Bauer committed
796
    relevant_strides = [stride for i, stride in enumerate(strides) if i not in index_dimension_ids]
797
    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
798
    return normalize_layout(result)
799
800


Martin Bauer's avatar
Martin Bauer committed
801
802
803
804
805
806
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
807
808
809
810
811

    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
812

Martin Bauer's avatar
Martin Bauer committed
813
    The index_dimension_ids parameter leaves specifies which coordinates should not be
Martin Bauer's avatar
Martin Bauer committed
814
    """
Martin Bauer's avatar
Martin Bauer committed
815
816
    index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
    return get_layout_from_strides(arr.strides, index_dimension_ids)
817
818


Martin Bauer's avatar
Martin Bauer committed
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
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)
835
836
    """
    assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
Martin Bauer's avatar
Martin Bauer committed
837
    cur_layout = list(range(len(shape)))
838
839
    swaps = []
    for i in range(len(layout)):
Martin Bauer's avatar
Martin Bauer committed
840
841
842
843
844
        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)
845
846
847
848
849

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

850
851
852
853
854
    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
855
        res = aligned_empty(shape, alignment, byte_offset=byte_offset, **kwargs)
856

857
858
859
860
861
    for a, b in reversed(swaps):
        res = res.swapaxes(a, b)
    return res


Martin Bauer's avatar
Martin Bauer committed
862
863
def spatial_layout_string_to_tuple(layout_str: str, dim: int) -> Tuple[int, ...]:
    if layout_str in ('fzyx', 'zyxf'):
864
865
        assert dim <= 3
        return tuple(reversed(range(dim)))
866

Martin Bauer's avatar
Martin Bauer committed
867
    if layout_str in ('fzyx', 'f', 'reverse_numpy', 'SoA'):
868
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
869
    elif layout_str in ('c', 'numpy', 'AoS'):
870
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
871
    raise ValueError("Unknown layout descriptor " + layout_str)
872
873


Martin Bauer's avatar
Martin Bauer committed
874
875
876
def layout_string_to_tuple(layout_str, dim):
    layout_str = layout_str.lower()
    if layout_str == 'fzyx' or layout_str == 'soa':
877
878
        assert dim <= 4
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
879
    elif layout_str == 'zyxf' or layout_str == 'aos':
880
        assert dim <= 4
Martin Bauer's avatar
Martin Bauer committed
881
        return tuple(reversed(range(dim - 1))) + (dim - 1,)
Martin Bauer's avatar
Martin Bauer committed
882
    elif layout_str == 'f' or layout_str == 'reverse_numpy':
883
        return tuple(reversed(range(dim)))
Martin Bauer's avatar
Martin Bauer committed
884
    elif layout_str == 'c' or layout_str == 'numpy':
885
        return tuple(range(dim))
Martin Bauer's avatar
Martin Bauer committed
886
    raise ValueError("Unknown layout descriptor " + layout_str)
887
888


Martin Bauer's avatar
Martin Bauer committed
889
def normalize_layout(layout):
890
    """Takes a layout tuple and subtracts the minimum from all entries"""
Martin Bauer's avatar
Martin Bauer committed
891
892
    min_entry = min(layout)
    return tuple(i - min_entry for i in layout)
893
894


Martin Bauer's avatar
Martin Bauer committed
895
def compute_strides(shape, layout):
896
897
    """
    Computes strides assuming no padding exists
Martin Bauer's avatar
Martin Bauer committed
898
899
900
901
902
903
904

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

    Returns:
        strides in elements, not in bytes
905
    """
Martin Bauer's avatar
Martin Bauer committed
906
907
908
909
    dim = len(shape)
    assert len(layout) == dim
    assert len(set(layout)) == dim
    strides = [0] * dim
910
    product = 1
911
    for j in reversed(layout):
912
913
914
        strides[j] = product
        product *= shape[j]
    return tuple(strides)
Martin Bauer's avatar
Martin Bauer committed
915
916


917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
# ---------------------------------------- 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)
941
942
943


def _parse_description(description):
944
945
946
    def parse_part1(d):
        result = field_description_regex.match(d)
        while result:
947
            name, index_str = result.group(1), result.group(2)
948
949
950
951
952
953
954
955
            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:
956
            data_type_str, size_info = result.group(1), result.group(2).strip().lower()
957
958
959
960
961
962
963
964
965
966
967
968
969
970
            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")

971
    if ':' in description:
972
        field_description, field_info = description.split(':')
973
    else:
974
975
976
977
978
        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")
979

980
981
    data_type, size = parse_part2(field_info)
    return fields_info, data_type, size