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