field.py 21.3 KB
Newer Older
1
2
3
4
5
from itertools import chain
import numpy as np
import sympy as sp
from sympy.core.cache import cacheit
from sympy.tensor import IndexedBase
6
from pystencils.data_types import TypedSymbol, createType
7
8


Michael Kuron's avatar
Michael Kuron committed
9
class Field(object):
10
11
12
13
    """
    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
14
15
16
17
    Creating Fields:

        To create a field use one of the static create* members. There are two options:

18
        1. create a kernel with fixed loop sizes i.e. the shape of the array is already known. This is usually the
Martin Bauer's avatar
Martin Bauer committed
19
           case if just-in-time compilation directly from Python is done. (see :func:`Field.createFromNumpyArray`)
20
        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
21
           beforehand for a library. (see :func:`Field.createGeneric`)
22
23
24
25
26
27

    Dimensions:
        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
        looped over. Additionally  N values are stored per cell. In this case spatialDimensions is two or three,
        and indexDimensions 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
28
        are four dimensions, two spatial and two index dimensions: ``len(arr.shape) == spatialDims + indexDims``
29
30
31
32

    Indexing:
        When accessing (indexing) a field the result is a FieldAccess which is derived from sympy Symbol.
        First specify the spatial offsets in [], then in case indexDimension>0 the indices in ()
Martin Bauer's avatar
Martin Bauer committed
33
        e.g. ``f[-1,0,0](7)``
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49

    Example without index dimensions:
        >>> a = np.zeros([10, 10])
        >>> f = Field.createFromNumpyArray("f", a, indexDimensions=0)
        >>> jacobi = ( f[-1,0] + f[1,0] + f[0,-1] + f[0,1] ) / 4

    Example with index dimensions: LBM D2Q9 stream pull
        >>> stencil = np.array([[0,0], [0,1], [0,-1]])
        >>> src = Field.createGeneric("src", spatialDimensions=2, indexDimensions=1)
        >>> dst = Field.createGeneric("dst", spatialDimensions=2, indexDimensions=1)
        >>> for i, offset in enumerate(stencil):
        ...     sp.Eq(dst[0,0](i), src[-offset](i))
        Eq(dst_C^0, src_C^0)
        Eq(dst_C^1, src_S^1)
        Eq(dst_C^2, src_N^2)
    """
50
51
52
53
54
55
56
57
58
59
60
61
62
63

    @staticmethod
    def createGeneric(fieldName, spatialDimensions, dtype=np.float64, indexDimensions=0, layout='numpy'):
        """
        Creates a generic field where the field size is not fixed i.e. can be called with arrays of different sizes

        :param fieldName: symbolic name for the field
        :param dtype: numpy data type of the array the kernel is called with later
        :param spatialDimensions: see documentation of Field
        :param indexDimensions: see documentation of Field
        :param 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
                       over dimension 0. Also allowed: the strings 'numpy' (0,1,..d) or 'reverseNumpy' (d, ..., 1, 0)
        """
64
        if isinstance(layout, str):
65
            layout = spatialLayoutStringToTuple(layout, dim=spatialDimensions)
66
67
68
69
70
        shapeSymbol = IndexedBase(TypedSymbol(Field.SHAPE_PREFIX + fieldName, Field.SHAPE_DTYPE), shape=(1,))
        strideSymbol = IndexedBase(TypedSymbol(Field.STRIDE_PREFIX + fieldName, Field.STRIDE_DTYPE), shape=(1,))
        totalDimensions = spatialDimensions + indexDimensions
        shape = tuple([shapeSymbol[i] for i in range(totalDimensions)])
        strides = tuple([strideSymbol[i] for i in range(totalDimensions)])
71
72
73
74
75
76
77
78

        npDataType = np.dtype(dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

79
80
        return Field(fieldName, dtype, layout, shape, strides)

81
82
83
84
85
86
87
88
89
90
91
92
93
    @staticmethod
    def createFromNumpyArray(fieldName, npArray, indexDimensions=0):
        """
        Creates a field based on the layout, data type, and shape of a given numpy array.
        Kernels created for these kind of fields can only be called with arrays of the same layout, shape and type.
        :param fieldName: symbolic name for the field
        :param npArray: numpy array
        :param indexDimensions: see documentation of Field
        """
        spatialDimensions = len(npArray.shape) - indexDimensions
        if spatialDimensions < 1:
            raise ValueError("Too many index dimensions. At least one spatial dimension required")

94
        fullLayout = getLayoutOfArray(npArray)
95
96
97
98
        spatialLayout = tuple([i for i in fullLayout if i < spatialDimensions])
        assert len(spatialLayout) == spatialDimensions

        strides = tuple([s // np.dtype(npArray.dtype).itemsize for s in npArray.strides])
99
        shape = tuple(int(s) for s in npArray.shape)
100

101
102
103
104
105
106
107
        npDataType = np.dtype(npArray.dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

108
109
110
        return Field(fieldName, npArray.dtype, spatialLayout, shape, strides)

    @staticmethod
111
    def createFixedSize(fieldName, shape, indexDimensions=0, dtype=np.float64, layout='numpy'):
112
        """
113
        Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout
114

115
        :param fieldName: symbolic name for the field
116
117
        :param shape: overall shape of the array
        :param indexDimensions: how many of the trailing dimensions are interpreted as index (as opposed to spatial)
118
        :param dtype: numpy data type of the array the kernel is called with later
119
        :param layout: full layout of array, not only spatial dimensions
120
        """
121
122
123
        spatialDimensions = len(shape) - indexDimensions
        assert spatialDimensions >= 1

124
        if isinstance(layout, str) and (layout == 'numpy' or layout.lower() == 'c'):
125
            layout = tuple(range(spatialDimensions))
126
        elif isinstance(layout, str) and (layout == 'reverseNumpy' or layout.lower() == 'f'):
Martin Bauer's avatar
Martin Bauer committed
127
            layout = tuple(reversed(range(spatialDimensions)))
128
129
130

        shape = tuple(int(s) for s in shape)
        strides = computeStrides(shape, layout)
131
132
133
134
135
136
137
138

        npDataType = np.dtype(dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

139
140
141
142
        spatialLayout = list(layout)
        for i in range(spatialDimensions, len(layout)):
            spatialLayout.remove(i)
        return Field(fieldName, dtype, tuple(spatialLayout), shape, strides)
143
144
145
146

    def __init__(self, fieldName, dtype, layout, shape, strides):
        """Do not use directly. Use static create* methods"""
        self._fieldName = fieldName
147
        self._dtype = createType(dtype)
148
        self._layout = normalizeLayout(layout)
149
150
        self.shape = shape
        self.strides = strides
151
152
153
        # 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
        self.isIndexField = False
154
155
156
157
158
159
160

    @property
    def spatialDimensions(self):
        return len(self._layout)

    @property
    def indexDimensions(self):
161
        return len(self.shape) - len(self._layout)
162
163
164
165
166
167
168
169
170
171
172

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

    @property
    def name(self):
        return self._fieldName

    @property
    def spatialShape(self):
173
        return self.shape[:self.spatialDimensions]
174

175
176
177
178
179
180
181
182
    @property
    def hasFixedShape(self):
        try:
            [int(i) for i in self.shape]
            return True
        except TypeError:
            return False

183
184
    @property
    def indexShape(self):
185
        return self.shape[self.spatialDimensions:]
186
187
188

    @property
    def spatialStrides(self):
189
        return self.strides[:self.spatialDimensions]
190
191
192

    @property
    def indexStrides(self):
193
        return self.strides[self.spatialDimensions:]
194
195
196
197
198
199
200
201

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

    def __repr__(self):
        return self._fieldName

202
203
204
205
206
    def neighbor(self, coordId, offset):
        offsetList = [0] * self.spatialDimensions
        offsetList[coordId] = offset
        return Field.Access(self, tuple(offsetList))

207
208
209
210
    def center(self):
        center = tuple([0] * self.spatialDimensions)
        return Field.Access(self, center)

211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
    def __getitem__(self, offset):
        if type(offset) is np.ndarray:
            offset = tuple(offset)
        if type(offset) is str:
            offset = tuple(directionStringToOffset(offset, self.spatialDimensions))
        if type(offset) is not tuple:
            offset = (offset,)
        if len(offset) != self.spatialDimensions:
            raise ValueError("Wrong number of spatial indices: "
                             "Got %d, expected %d" % (len(offset), self.spatialDimensions))
        return Field.Access(self, offset)

    def __call__(self, *args, **kwargs):
        center = tuple([0]*self.spatialDimensions)
        return Field.Access(self, center)(*args, **kwargs)

    def __hash__(self):
228
        return hash((self._layout, self.shape, self.strides, self._dtype, self._fieldName))
229
230
231
232
233
234
235
236
237
238
239

    def __eq__(self, other):
        selfTuple = (self.shape, self.strides, self.name, self.dtype)
        otherTuple = (other.shape, other.strides, other.name, other.dtype)
        return selfTuple == otherTuple

    PREFIX = "f"
    STRIDE_PREFIX = PREFIX + "stride_"
    SHAPE_PREFIX = PREFIX + "shape_"
    STRIDE_DTYPE = "const int *"
    SHAPE_DTYPE = "const int *"
240
    DATA_PREFIX = PREFIX + "d_"
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257

    class Access(sp.Symbol):
        def __new__(cls, name, *args, **kwargs):
            obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
            return obj

        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None):
            fieldName = field.name
            offsetsAndIndex = chain(offsets, idx) if idx is not None else offsets
            constantOffsets = not any([isinstance(o, sp.Basic) for o in offsetsAndIndex])

            if not idx:
                idx = tuple([0] * field.indexDimensions)

            if constantOffsets:
                offsetName = offsetToDirectionString(offsets)
                if field.indexDimensions == 0:
258
                    superscript = None
259
                elif field.indexDimensions == 1:
260
                    superscript = str(idx[0])
261
262
                else:
                    idxStr = ",".join([str(e) for e in idx])
263
                    superscript = idxStr
264
265
            else:
                offsetName = "%0.10X" % (abs(hash(tuple(offsetsAndIndex))))
266
                superscript = None
267

268
269
270
271
272
            symbolName = "%s_%s" % (fieldName, offsetName)
            if superscript is not None:
                symbolName += "^" + superscript

            obj = super(Field.Access, self).__xnew__(self, symbolName)
273
274
275
276
277
278
279
280
            obj._field = field
            obj._offsets = []
            for o in offsets:
                if isinstance(o, sp.Basic):
                    obj._offsets.append(o)
                else:
                    obj._offsets.append(int(o))
            obj._offsetName = offsetName
281
            obj._superscript = superscript
282
283
284
285
            obj._index = idx

            return obj

286
        def __getnewargs__(self):
287
            return self.field, self.offsets, self.index
288

289
290
291
292
293
294
295
296
297
298
299
300
301
302
        __xnew__ = staticmethod(__new_stage2__)
        __xnew_cached_ = staticmethod(cacheit(__new_stage2__))

        def __call__(self, *idx):
            if self._index != tuple([0]*self.field.indexDimensions):
                print(self._index, tuple([0]*self.field.indexDimensions))
                raise ValueError("Indexing an already indexed Field.Access")

            idx = tuple(idx)
            if len(idx) != self.field.indexDimensions and idx != (0,):
                raise ValueError("Wrong number of indices: "
                                 "Got %d, expected %d" % (len(idx), self.field.indexDimensions))
            return Field.Access(self.field, self._offsets, idx)

Martin Bauer's avatar
Martin Bauer committed
303
304
305
        def __getitem__(self, *idx):
            return self.__call__(*idx)

Martin Bauer's avatar
Martin Bauer committed
306
307
308
309
310
        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")

311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
        @property
        def field(self):
            return self._field

        @property
        def offsets(self):
            return self._offsets

        @property
        def requiredGhostLayers(self):
            return int(np.max(np.abs(self._offsets)))

        @property
        def nrOfCoordinates(self):
            return len(self._offsets)

        @property
        def offsetName(self):
            return self._offsetName

331
332
333
334
335
336
        def _latex(self, arg):
            if self._superscript:
                return "{{%s}_{%s}^{%s}}" % (self._field.name, self._offsetName, self._superscript)
            else:
                return "{{%s}_{%s}}" % (self._field.name, self._offsetName)

337
338
339
340
        @property
        def index(self):
            return self._index

341
342
343
344
345
346
        def getNeighbor(self, *offsets):
            return Field.Access(self.field, offsets, self.index)

        def getShifted(self, *shift):
            return Field.Access(self.field, tuple(a + b for a, b in zip(shift, self.offsets)), self.index)

347
348
        def _hashable_content(self):
            superClassContents = list(super(Field.Access, self)._hashable_content())
Martin Bauer's avatar
Martin Bauer committed
349
            t = tuple(superClassContents + [hash(self._field), self._index] + self._offsets)
350
            return t
Martin Bauer's avatar
Martin Bauer committed
351
352
353
354
355
356
357
358
359


def extractCommonSubexpressions(equations):
    """
    Uses sympy to find common subexpressions in equations and returns
    them in a topologically sorted order, ready for evaluation.
    Usually called before list of equations is passed to :func:`createKernel`
    """
    replacements, newEq = sp.cse(equations)
Martin Bauer's avatar
Martin Bauer committed
360
361
362
363
364
    # Workaround for older sympy versions: here subexpressions (temporary = True) are extracted
    # which leads to problems in Piecewise functions which have to a default case indicated by True
    symbolsEqualToTrue = {r[0]: True for r in replacements if r[1] is sp.true}

    replacementEqs = [sp.Eq(*r) for r in replacements if r[1] is not sp.true]
Martin Bauer's avatar
Martin Bauer committed
365
366
    equations = replacementEqs + newEq
    topologicallySortedPairs = sp.cse_main.reps_toposort([[e.lhs, e.rhs] for e in equations])
Martin Bauer's avatar
Martin Bauer committed
367
    equations = [sp.Eq(a[0], a[1].subs(symbolsEqualToTrue)) for a in topologicallySortedPairs]
Martin Bauer's avatar
Martin Bauer committed
368
369
370
    return equations


371
372
373
374
375
376
377
def getLayoutFromStrides(strides, indexDimensionIds=[]):
    coordinates = list(range(len(strides)))
    relevantStrides = [stride for i, stride in enumerate(strides) if i not in indexDimensionIds]
    result = [x for (y, x) in sorted(zip(relevantStrides, coordinates), key=lambda pair: pair[0], reverse=True)]
    return normalizeLayout(result)


378
def getLayoutOfArray(arr, indexDimensionIds=[]):
Martin Bauer's avatar
Martin Bauer committed
379
380
381
    """
    Returns a list indicating the memory layout (linearization order) of the numpy array.
    Example:
382
    >>> getLayoutOfArray(np.zeros([3,3,3]))
Martin Bauer's avatar
Martin Bauer committed
383
    (0, 1, 2)
Martin Bauer's avatar
Martin Bauer committed
384
385
386
387
388

    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
389
390

    The indexDimensionIds parameter leaves specifies which coordinates should not be
Martin Bauer's avatar
Martin Bauer committed
391
    """
392
    return getLayoutFromStrides(arr.strides, indexDimensionIds)
393
394


395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
def createNumpyArrayWithLayout(shape, layout):
    """
    Creates a numpy array with
    :param shape: shape of the resulting array
    :param layout: layout as tuple, where the coordinates are ordered from slow to fast
    >>> res = createNumpyArrayWithLayout(shape=(2, 3, 4, 5), layout=(3, 2, 0, 1))
    >>> res.shape
    (2, 3, 4, 5)
    >>> getLayoutOfArray(res)
    (3, 2, 0, 1)
    """
    assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
    currentLayout = list(range(len(shape)))
    swaps = []
    for i in range(len(layout)):
        if currentLayout[i] != layout[i]:
            indexToSwapWith = currentLayout.index(layout[i])
            swaps.append((i, indexToSwapWith))
            currentLayout[i], currentLayout[indexToSwapWith] = currentLayout[indexToSwapWith], currentLayout[i]
    assert tuple(currentLayout) == tuple(layout)

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

    res = np.empty(shape, order='c')
    for a, b in reversed(swaps):
        res = res.swapaxes(a, b)
    return res


426
427
428
429
def spatialLayoutStringToTuple(layoutStr, dim):
    if layoutStr in ('fzyx', 'zyxf'):
        assert dim <= 3
        return tuple(reversed(range(dim)))
430
431
432
433
434

    if layoutStr == "fzyx" or layoutStr == 'f' or layoutStr == 'reverseNumpy':
        return tuple(reversed(range(dim)))
    elif layoutStr == 'c' or layoutStr == 'numpy':
        return tuple(range(dim))
435
436
437
438
439
440
441
    raise ValueError("Unknown layout descriptor " + layoutStr)


def layoutStringToTuple(layoutStr, dim):
    if layoutStr == 'fzyx':
        assert dim <= 4
        return tuple(reversed(range(dim)))
442
    elif layoutStr == 'zyxf':
443
444
445
446
447
448
        assert dim <= 4
        return tuple(reversed(range(dim - 1))) + (dim-1,)
    elif layoutStr == 'f' or layoutStr == 'reverseNumpy':
        return tuple(reversed(range(dim)))
    elif layoutStr == 'c' or layoutStr == 'numpy':
        return tuple(range(dim))
449
450
451
    raise ValueError("Unknown layout descriptor " + layoutStr)


452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
def normalizeLayout(layout):
    """Takes a layout tuple and subtracts the minimum from all entries"""
    minEntry = min(layout)
    return tuple(i - minEntry for i in layout)


def computeStrides(shape, layout):
    """
    Computes strides assuming no padding exists
    :param shape: shape (size) of array
    :param layout: layout specification as tuple
    :return: strides in elements, not in bytes
    """
    N = len(shape)
    assert len(layout) == N
    assert len(set(layout)) == N
    strides = [0] * N
    product = 1
470
    for j in reversed(layout):
471
472
473
        strides[j] = product
        product *= shape[j]
    return tuple(strides)
Martin Bauer's avatar
Martin Bauer committed
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
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
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
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566


def offsetComponentToDirectionString(coordinateId, value):
    """
    Translates numerical offset to string notation.
    x offsets are labeled with east 'E' and 'W',
    y offsets with north 'N' and 'S' and
    z offsets with top 'T' and bottom 'B'
    If the absolute value of the offset is bigger than 1, this number is prefixed.
    :param coordinateId: integer 0, 1 or 2 standing for x,y and z
    :param value: integer offset

    Example:
    >>> offsetComponentToDirectionString(0, 1)
    'E'
    >>> offsetComponentToDirectionString(1, 2)
    '2N'
    """
    nameComponents = (('W', 'E'),  # west, east
                      ('S', 'N'),  # south, north
                      ('B', 'T'),  # bottom, top
                      )
    if value == 0:
        result = ""
    elif value < 0:
        result = nameComponents[coordinateId][0]
    else:
        result = nameComponents[coordinateId][1]
    if abs(value) > 1:
        result = "%d%s" % (abs(value), result)
    return result


def offsetToDirectionString(offsetTuple):
    """
    Translates numerical offset to string notation.
    For details see :func:`offsetComponentToDirectionString`
    :param offsetTuple: 3-tuple with x,y,z offset

    Example:
    >>> offsetToDirectionString([1, -1, 0])
    'SE'
    >>> offsetToDirectionString(([-3, 0, -2]))
    '2B3W'
    """
    names = ["", "", ""]
    for i in range(len(offsetTuple)):
        names[i] = offsetComponentToDirectionString(i, offsetTuple[i])
    name = "".join(reversed(names))
    if name == "":
        name = "C"
    return name


def directionStringToOffset(directionStr, dim=3):
    """
    Reverse mapping of :func:`offsetToDirectionString`
    :param directionStr: string representation of offset
    :param dim: dimension of offset, i.e the length of the returned list

    >>> directionStringToOffset('NW', dim=3)
    array([-1,  1,  0])
    >>> directionStringToOffset('NW', dim=2)
    array([-1,  1])
    >>> directionStringToOffset(offsetToDirectionString([3,-2,1]))
    array([ 3, -2,  1])
    """
    offsetMap = {
        'C': np.array([0, 0, 0]),

        'W': np.array([-1, 0, 0]),
        'E': np.array([1, 0, 0]),

        'S': np.array([0, -1, 0]),
        'N': np.array([0, 1, 0]),

        'B': np.array([0, 0, -1]),
        'T': np.array([0, 0, 1]),
    }
    offset = np.array([0, 0, 0])

    while len(directionStr) > 0:
        factor = 1
        firstNonDigit = 0
        while directionStr[firstNonDigit].isdigit():
            firstNonDigit += 1
        if firstNonDigit > 0:
            factor = int(directionStr[:firstNonDigit])
            directionStr = directionStr[firstNonDigit:]
        curOffset = offsetMap[directionStr[0]]
        offset += factor * curOffset
        directionStr = directionStr[1:]
    return offset[:dim]
567
568
569
570
571
572
573


if __name__ == '__main__':
    f = Field.createGeneric('f', spatialDimensions=2, indexDimensions=1)
    fa = f[0, 1](4) ** 2
    print(fa)
    print(sp.latex(fa))