fdb0ab0863e83fe33c262c8e3fb6207cca267802
[linpy.git] / pypol / domains.py
1 import ast
2 import functools
3 import re
4
5 from fractions import Fraction
6
7 from . import islhelper
8 from .islhelper import mainctx, libisl, isl_set_basic_sets
9 from .linexprs import Expression, Symbol
10
11
12 __all__ = [
13 'Domain',
14 'And', 'Or', 'Not',
15 ]
16
17
18 @functools.total_ordering
19 class Domain:
20
21 __slots__ = (
22 '_polyhedra',
23 '_symbols',
24 '_dimension',
25 )
26
27 def __new__(cls, *polyhedra):
28 from .polyhedra import Polyhedron
29 if len(polyhedra) == 1:
30 polyhedron = polyhedra[0]
31 if isinstance(polyhedron, str):
32 return cls.fromstring(polyhedron)
33 elif isinstance(polyhedron, Polyhedron):
34 return polyhedron
35 else:
36 raise TypeError('argument must be a string '
37 'or a Polyhedron instance')
38 else:
39 for polyhedron in polyhedra:
40 if not isinstance(polyhedron, Polyhedron):
41 raise TypeError('arguments must be Polyhedron instances')
42 symbols = cls._xsymbols(polyhedra)
43 islset = cls._toislset(polyhedra, symbols)
44 return cls._fromislset(islset, symbols)
45
46 @classmethod
47 def _xsymbols(cls, iterator):
48 """
49 Return the ordered tuple of symbols present in iterator.
50 """
51 symbols = set()
52 for item in iterator:
53 symbols.update(item.symbols)
54 return tuple(sorted(symbols, key=Symbol.sortkey))
55
56 @property
57 def polyhedra(self):
58 return self._polyhedra
59
60 @property
61 def symbols(self):
62 return self._symbols
63
64 @property
65 def dimension(self):
66 return self._dimension
67
68 def disjoint(self):
69 islset = self._toislset(self.polyhedra, self.symbols)
70 islset = libisl.isl_set_make_disjoint(mainctx, islset)
71 return self._fromislset(islset, self.symbols)
72
73 def isempty(self):
74 islset = self._toislset(self.polyhedra, self.symbols)
75 empty = bool(libisl.isl_set_is_empty(islset))
76 libisl.isl_set_free(islset)
77 return empty
78
79 def __bool__(self):
80 return not self.isempty()
81
82 def isuniverse(self):
83 islset = self._toislset(self.polyhedra, self.symbols)
84 universe = bool(libisl.isl_set_plain_is_universe(islset))
85 libisl.isl_set_free(islset)
86 return universe
87
88 def isbounded(self):
89 islset = self._toislset(self.polyhedra, self.symbols)
90 bounded = bool(libisl.isl_set_is_bounded(islset))
91 libisl.isl_set_free(islset)
92 return bounded
93
94 def __eq__(self, other):
95 symbols = self._xsymbols([self, other])
96 islset1 = self._toislset(self.polyhedra, symbols)
97 islset2 = other._toislset(other.polyhedra, symbols)
98 equal = bool(libisl.isl_set_is_equal(islset1, islset2))
99 libisl.isl_set_free(islset1)
100 libisl.isl_set_free(islset2)
101 return equal
102
103 def isdisjoint(self, other):
104 symbols = self._xsymbols([self, other])
105 islset1 = self._toislset(self.polyhedra, symbols)
106 islset2 = self._toislset(other.polyhedra, symbols)
107 equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
108 libisl.isl_set_free(islset1)
109 libisl.isl_set_free(islset2)
110 return equal
111
112 def issubset(self, other):
113 symbols = self._xsymbols([self, other])
114 islset1 = self._toislset(self.polyhedra, symbols)
115 islset2 = self._toislset(other.polyhedra, symbols)
116 equal = bool(libisl.isl_set_is_subset(islset1, islset2))
117 libisl.isl_set_free(islset1)
118 libisl.isl_set_free(islset2)
119 return equal
120
121 def __le__(self, other):
122 return self.issubset(other)
123
124 def __lt__(self, other):
125 symbols = self._xsymbols([self, other])
126 islset1 = self._toislset(self.polyhedra, symbols)
127 islset2 = self._toislset(other.polyhedra, symbols)
128 equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
129 libisl.isl_set_free(islset1)
130 libisl.isl_set_free(islset2)
131 return equal
132
133 def complement(self):
134 islset = self._toislset(self.polyhedra, self.symbols)
135 islset = libisl.isl_set_complement(islset)
136 return self._fromislset(islset, self.symbols)
137
138 def __invert__(self):
139 return self.complement()
140
141 def simplify(self):
142 #does not change anything in any of the examples
143 #isl seems to do this naturally
144 islset = self._toislset(self.polyhedra, self.symbols)
145 islset = libisl.isl_set_remove_redundancies(islset)
146 return self._fromislset(islset, self.symbols)
147
148 def aspolyhedron(self):
149 # several types of hull are available
150 # polyhedral seems to be the more appropriate, to be checked
151 from .polyhedra import Polyhedron
152 islset = self._toislset(self.polyhedra, self.symbols)
153 islbset = libisl.isl_set_polyhedral_hull(islset)
154 return Polyhedron._fromislbasicset(islbset, self.symbols)
155
156 def project(self, dims):
157 # use to remove certain variables
158 islset = self._toislset(self.polyhedra, self.symbols)
159 n = 0
160 for index, symbol in reversed(list(enumerate(self.symbols))):
161 if symbol in dims:
162 n += 1
163 elif n > 0:
164 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
165 n = 0
166 if n > 0:
167 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
168 dims = [symbol for symbol in self.symbols if symbol not in dims]
169 return Domain._fromislset(islset, dims)
170
171 def sample(self):
172 islset = self._toislset(self.polyhedra, self.symbols)
173 islpoint = libisl.isl_set_sample_point(islset)
174 if bool(libisl.isl_point_is_void(islpoint)):
175 libisl.isl_point_free(islpoint)
176 raise ValueError('domain must be non-empty')
177 point = {}
178 for index, symbol in enumerate(self.symbols):
179 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
180 libisl.isl_dim_set, index)
181 coordinate = islhelper.isl_val_to_int(coordinate)
182 point[symbol] = coordinate
183 libisl.isl_point_free(islpoint)
184 return point
185
186 def intersection(self, *others):
187 if len(others) == 0:
188 return self
189 symbols = self._xsymbols((self,) + others)
190 islset1 = self._toislset(self.polyhedra, symbols)
191 for other in others:
192 islset2 = other._toislset(other.polyhedra, symbols)
193 islset1 = libisl.isl_set_intersect(islset1, islset2)
194 return self._fromislset(islset1, symbols)
195
196 def __and__(self, other):
197 return self.intersection(other)
198
199 def union(self, *others):
200 if len(others) == 0:
201 return self
202 symbols = self._xsymbols((self,) + others)
203 islset1 = self._toislset(self.polyhedra, symbols)
204 for other in others:
205 islset2 = other._toislset(other.polyhedra, symbols)
206 islset1 = libisl.isl_set_union(islset1, islset2)
207 return self._fromislset(islset1, symbols)
208
209 def __or__(self, other):
210 return self.union(other)
211
212 def __add__(self, other):
213 return self.union(other)
214
215 def difference(self, other):
216 symbols = self._xsymbols([self, other])
217 islset1 = self._toislset(self.polyhedra, symbols)
218 islset2 = other._toislset(other.polyhedra, symbols)
219 islset = libisl.isl_set_subtract(islset1, islset2)
220 return self._fromislset(islset, symbols)
221
222 def __sub__(self, other):
223 return self.difference(other)
224
225 def lexmin(self):
226 islset = self._toislset(self.polyhedra, self.symbols)
227 islset = libisl.isl_set_lexmin(islset)
228 return self._fromislset(islset, self.symbols)
229
230 def lexmax(self):
231 islset = self._toislset(self.polyhedra, self.symbols)
232 islset = libisl.isl_set_lexmax(islset)
233 return self._fromislset(islset, self.symbols)
234
235 def num_parameters(self):
236 #could be useful with large, complicated polyhedrons
237 islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
238 num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
239 return num
240
241 def involves_dims(self, dims):
242 #could be useful with large, complicated polyhedrons
243 islset = self._toislset(self.polyhedra, self.symbols)
244 dims = sorted(dims)
245 symbols = sorted(list(self.symbols))
246 n = 0
247 if len(dims)>0:
248 for dim in dims:
249 if dim in symbols:
250 first = symbols.index(dims[0])
251 n +=1
252 else:
253 first = 0
254 else:
255 return False
256 value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
257 libisl.isl_set_free(islset)
258 return value
259
260 _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
261
262 def vertices(self):
263 islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
264 vertices = libisl.isl_basic_set_compute_vertices(islbset);
265 vertices = islhelper.isl_vertices_vertices(vertices)
266 points = []
267 for vertex in vertices:
268 expr = libisl.isl_vertex_get_expr(vertex);
269 if islhelper.isl_version < '0.13':
270 string = islhelper.isl_set_to_str(expr)
271 print(string)
272 # to be continued...
273 else:
274 # horrible hack, find a cleaner solution
275 string = islhelper.isl_multi_aff_to_str(expr)
276 matches = self._RE_COORDINATE.finditer(string)
277 point = {}
278 for symbol, match in zip(self.symbols, matches):
279 numerator = int(match.group('num'))
280 denominator = match.group('den')
281 denominator = 1 if denominator is None else int(denominator)
282 coordinate = Fraction(numerator, denominator)
283 point[symbol] = coordinate
284 points.append(point)
285 return points
286
287 def points(self):
288 if not self.isbounded():
289 raise ValueError('domain must be bounded')
290 from .polyhedra import Universe, Eq
291 islset = self._toislset(self.polyhedra, self.symbols)
292 islpoints = islhelper.isl_set_points(islset)
293 points = []
294 for islpoint in islpoints:
295 point = {}
296 for index, symbol in enumerate(self.symbols):
297 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
298 libisl.isl_dim_set, index)
299 coordinate = islhelper.isl_val_to_int(coordinate)
300 point[symbol] = coordinate
301 points.append(point)
302 return points
303
304 @classmethod
305 def _fromislset(cls, islset, symbols):
306 from .polyhedra import Polyhedron
307 islset = libisl.isl_set_remove_divs(islset)
308 islbsets = isl_set_basic_sets(islset)
309 libisl.isl_set_free(islset)
310 polyhedra = []
311 for islbset in islbsets:
312 polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
313 polyhedra.append(polyhedron)
314 if len(polyhedra) == 0:
315 from .polyhedra import Empty
316 return Empty
317 elif len(polyhedra) == 1:
318 return polyhedra[0]
319 else:
320 self = object().__new__(Domain)
321 self._polyhedra = tuple(polyhedra)
322 self._symbols = cls._xsymbols(polyhedra)
323 self._dimension = len(self._symbols)
324 return self
325
326 def _toislset(cls, polyhedra, symbols):
327 polyhedron = polyhedra[0]
328 islbset = polyhedron._toislbasicset(polyhedron.equalities,
329 polyhedron.inequalities, symbols)
330 islset1 = libisl.isl_set_from_basic_set(islbset)
331 for polyhedron in polyhedra[1:]:
332 islbset = polyhedron._toislbasicset(polyhedron.equalities,
333 polyhedron.inequalities, symbols)
334 islset2 = libisl.isl_set_from_basic_set(islbset)
335 islset1 = libisl.isl_set_union(islset1, islset2)
336 return islset1
337
338 @classmethod
339 def _fromast(cls, node):
340 from .polyhedra import Polyhedron
341 if isinstance(node, ast.Module) and len(node.body) == 1:
342 return cls._fromast(node.body[0])
343 elif isinstance(node, ast.Expr):
344 return cls._fromast(node.value)
345 elif isinstance(node, ast.UnaryOp):
346 domain = cls._fromast(node.operand)
347 if isinstance(node.operand, ast.invert):
348 return Not(domain)
349 elif isinstance(node, ast.BinOp):
350 domain1 = cls._fromast(node.left)
351 domain2 = cls._fromast(node.right)
352 if isinstance(node.op, ast.BitAnd):
353 return And(domain1, domain2)
354 elif isinstance(node.op, ast.BitOr):
355 return Or(domain1, domain2)
356 elif isinstance(node, ast.Compare):
357 equalities = []
358 inequalities = []
359 left = Expression._fromast(node.left)
360 for i in range(len(node.ops)):
361 op = node.ops[i]
362 right = Expression._fromast(node.comparators[i])
363 if isinstance(op, ast.Lt):
364 inequalities.append(right - left - 1)
365 elif isinstance(op, ast.LtE):
366 inequalities.append(right - left)
367 elif isinstance(op, ast.Eq):
368 equalities.append(left - right)
369 elif isinstance(op, ast.GtE):
370 inequalities.append(left - right)
371 elif isinstance(op, ast.Gt):
372 inequalities.append(left - right - 1)
373 else:
374 break
375 left = right
376 else:
377 return Polyhedron(equalities, inequalities)
378 raise SyntaxError('invalid syntax')
379
380 _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
381 _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
382 _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
383 _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
384 _RE_NOT = re.compile(r'\bnot\b|!|¬')
385 _RE_NUM_VAR = Expression._RE_NUM_VAR
386 _RE_OPERATORS = re.compile(r'(&|\||~)')
387
388 @classmethod
389 def fromstring(cls, string):
390 # remove curly brackets
391 string = cls._RE_BRACES.sub(r'', string)
392 # replace '=' by '=='
393 string = cls._RE_EQ.sub(r'\1==\2', string)
394 # replace 'and', 'or', 'not'
395 string = cls._RE_AND.sub(r' & ', string)
396 string = cls._RE_OR.sub(r' | ', string)
397 string = cls._RE_NOT.sub(r' ~', string)
398 # add implicit multiplication operators, e.g. '5x' -> '5*x'
399 string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
400 # add parentheses to force precedence
401 tokens = cls._RE_OPERATORS.split(string)
402 for i, token in enumerate(tokens):
403 if i % 2 == 0:
404 token = '({})'.format(token)
405 tokens[i] = token
406 string = ''.join(tokens)
407 tree = ast.parse(string, 'eval')
408 return cls._fromast(tree)
409
410 def __repr__(self):
411 assert len(self.polyhedra) >= 2
412 strings = [repr(polyhedron) for polyhedron in self.polyhedra]
413 return 'Or({})'.format(', '.join(strings))
414
415 @classmethod
416 def fromsympy(cls, expr):
417 import sympy
418 from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
419 funcmap = {
420 sympy.And: And, sympy.Or: Or, sympy.Not: Not,
421 sympy.Lt: Lt, sympy.Le: Le,
422 sympy.Eq: Eq, sympy.Ne: Ne,
423 sympy.Ge: Ge, sympy.Gt: Gt,
424 }
425 if expr.func in funcmap:
426 args = [Domain.fromsympy(arg) for arg in expr.args]
427 return funcmap[expr.func](*args)
428 elif isinstance(expr, sympy.Expr):
429 return Expression.fromsympy(expr)
430 raise ValueError('non-domain expression: {!r}'.format(expr))
431
432 def tosympy(self):
433 import sympy
434 polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
435 return sympy.Or(*polyhedra)
436
437
438 def And(*domains):
439 if len(domains) == 0:
440 from .polyhedra import Universe
441 return Universe
442 else:
443 return domains[0].intersection(*domains[1:])
444
445 def Or(*domains):
446 if len(domains) == 0:
447 from .polyhedra import Empty
448 return Empty
449 else:
450 return domains[0].union(*domains[1:])
451
452 def Not(domain):
453 return ~domain