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
   9 from .geometry import GeometricObject, Point
  10 from .linexprs import Expression, Symbol
  11
  12
  13 __all__ = [
  14     'Domain',
  15     'And', 'Or', 'Not',
  16 ]
  17
  18
  19 @functools.total_ordering
  20 class Domain(GeometricObject):
  21
  22     __slots__ = (
  23         '_polyhedra',
  24         '_symbols',
  25         '_dimension',
  26     )
  27
  28     def __new__(cls, *polyhedra):
  29         from .polyhedra import Polyhedron
  30         if len(polyhedra) == 1:
  31             argument = polyhedra[0]
  32             if isinstance(argument, str):
  33                 return cls.fromstring(argument)
  34             elif isinstance(argument, GeometricObject):
  35                 return argument.aspolyhedron()
  36             else:
  37                 raise TypeError('argument must be a string '
  38                     'or a GeometricObject instance')
  39         else:
  40             for polyhedron in polyhedra:
  41                 if not isinstance(polyhedron, Polyhedron):
  42                     raise TypeError('arguments must be Polyhedron instances')
  43             symbols = cls._xsymbols(polyhedra)
  44             islset = cls._toislset(polyhedra, symbols)
  45             return cls._fromislset(islset, symbols)
  46
  47     @classmethod
  48     def _xsymbols(cls, iterator):
  49         """
  50         Return the ordered tuple of symbols present in iterator.
  51         """
  52         symbols = set()
  53         for item in iterator:
  54             symbols.update(item.symbols)
  55         return tuple(sorted(symbols, key=Symbol.sortkey))
  56
  57     @property
  58     def polyhedra(self):
  59         return self._polyhedra
  60
  61     @property
  62     def symbols(self):
  63         return self._symbols
  64
  65     @property
  66     def dimension(self):
  67         return self._dimension
  68
  69     def disjoint(self):
  70         """
  71         Returns this set as disjoint.
  72         """
  73         islset = self._toislset(self.polyhedra, self.symbols)
  74         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  75         return self._fromislset(islset, self.symbols)
  76
  77     def isempty(self):
  78         """
  79         Returns true if this set is an Empty set.
  80         """
  81         islset = self._toislset(self.polyhedra, self.symbols)
  82         empty = bool(libisl.isl_set_is_empty(islset))
  83         libisl.isl_set_free(islset)
  84         return empty
  85
  86     def __bool__(self):
  87         return not self.isempty()
  88
  89     def isuniverse(self):
  90         """
  91         Returns true if this set is the Universe set.
  92         """
  93         islset = self._toislset(self.polyhedra, self.symbols)
  94         universe = bool(libisl.isl_set_plain_is_universe(islset))
  95         libisl.isl_set_free(islset)
  96         return universe
  97
  98     def isbounded(self):
  99         """
 100         Returns true if this set is bounded.
 101         """
 102         islset = self._toislset(self.polyhedra, self.symbols)
 103         bounded = bool(libisl.isl_set_is_bounded(islset))
 104         libisl.isl_set_free(islset)
 105         return bounded
 106
 107     def __eq__(self, other):
 108         """
 109         Returns true if two sets are equal.
 110         """
 111         symbols = self._xsymbols([self, other])
 112         islset1 = self._toislset(self.polyhedra, symbols)
 113         islset2 = other._toislset(other.polyhedra, symbols)
 114         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
 115         libisl.isl_set_free(islset1)
 116         libisl.isl_set_free(islset2)
 117         return equal
 118
 119     def isdisjoint(self, other):
 120         """
 121         Return True if two sets have a null intersection.
 122         """
 123         symbols = self._xsymbols([self, other])
 124         islset1 = self._toislset(self.polyhedra, symbols)
 125         islset2 = self._toislset(other.polyhedra, symbols)
 126         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 127         libisl.isl_set_free(islset1)
 128         libisl.isl_set_free(islset2)
 129         return equal
 130
 131     def issubset(self, other):
 132         """
 133         Report whether another set contains this set.
 134         """
 135         symbols = self._xsymbols([self, other])
 136         islset1 = self._toislset(self.polyhedra, symbols)
 137         islset2 = self._toislset(other.polyhedra, symbols)
 138         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 139         libisl.isl_set_free(islset1)
 140         libisl.isl_set_free(islset2)
 141         return equal
 142
 143     def __le__(self, other):
 144         """
 145         Returns true if this set is less than or equal to another set.
 146         """
 147         return self.issubset(other)
 148
 149     def __lt__(self, other):
 150         """
 151         Returns true if this set is less than another set.
 152         """
 153         symbols = self._xsymbols([self, other])
 154         islset1 = self._toislset(self.polyhedra, symbols)
 155         islset2 = self._toislset(other.polyhedra, symbols)
 156         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 157         libisl.isl_set_free(islset1)
 158         libisl.isl_set_free(islset2)
 159         return equal
 160
 161     def complement(self):
 162         """
 163         Returns the complement of this set.
 164         """
 165         islset = self._toislset(self.polyhedra, self.symbols)
 166         islset = libisl.isl_set_complement(islset)
 167         return self._fromislset(islset, self.symbols)
 168
 169     def __invert__(self):
 170         """
 171         Returns the complement of this set.
 172         """
 173         return self.complement()
 174
 175     def simplify(self):
 176         """
 177         Returns a set without redundant constraints.
 178         """
 179         islset = self._toislset(self.polyhedra, self.symbols)
 180         islset = libisl.isl_set_remove_redundancies(islset)
 181         return self._fromislset(islset, self.symbols)
 182
 183     def aspolyhedron(self):
 184         """
 185         Returns polyhedral hull of set.
 186         """
 187         from .polyhedra import Polyhedron
 188         islset = self._toislset(self.polyhedra, self.symbols)
 189         islbset = libisl.isl_set_polyhedral_hull(islset)
 190         return Polyhedron._fromislbasicset(islbset, self.symbols)
 191
 192     def asdomain(self):
 193         return self
 194
 195     def project(self, dims):
 196         """
 197         Return new set with given dimensions removed.
 198         """
 199         islset = self._toislset(self.polyhedra, self.symbols)
 200         n = 0
 201         for index, symbol in reversed(list(enumerate(self.symbols))):
 202             if symbol in dims:
 203                 n += 1
 204             elif n > 0:
 205                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 206                 n = 0
 207         if n > 0:
 208             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 209         dims = [symbol for symbol in self.symbols if symbol not in dims]
 210         return Domain._fromislset(islset, dims)
 211
 212     def sample(self):
 213         """
 214         Returns a single subset of the input.
 215         """
 216         islset = self._toislset(self.polyhedra, self.symbols)
 217         islpoint = libisl.isl_set_sample_point(islset)
 218         if bool(libisl.isl_point_is_void(islpoint)):
 219             libisl.isl_point_free(islpoint)
 220             raise ValueError('domain must be non-empty')
 221         point = {}
 222         for index, symbol in enumerate(self.symbols):
 223             coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 224                 libisl.isl_dim_set, index)
 225             coordinate = islhelper.isl_val_to_int(coordinate)
 226             point[symbol] = coordinate
 227         libisl.isl_point_free(islpoint)
 228         return point
 229
 230     def intersection(self, *others):
 231         """
 232          Return the intersection of two sets as a new set.
 233         """
 234         if len(others) == 0:
 235             return self
 236         symbols = self._xsymbols((self,) + others)
 237         islset1 = self._toislset(self.polyhedra, symbols)
 238         for other in others:
 239             islset2 = other._toislset(other.polyhedra, symbols)
 240             islset1 = libisl.isl_set_intersect(islset1, islset2)
 241         return self._fromislset(islset1, symbols)
 242
 243     def __and__(self, other):
 244         """
 245          Return the intersection of two sets as a new set.
 246         """
 247         return self.intersection(other)
 248
 249     def union(self, *others):
 250         """
 251         Return the union of sets as a new set.
 252         """
 253         if len(others) == 0:
 254             return self
 255         symbols = self._xsymbols((self,) + others)
 256         islset1 = self._toislset(self.polyhedra, symbols)
 257         for other in others:
 258             islset2 = other._toislset(other.polyhedra, symbols)
 259             islset1 = libisl.isl_set_union(islset1, islset2)
 260         return self._fromislset(islset1, symbols)
 261
 262     def __or__(self, other):
 263         """
 264         Return a new set with elements from both sets.
 265         """
 266         return self.union(other)
 267
 268     def __add__(self, other):
 269         """
 270         Return new set containing all elements in both sets.
 271         """
 272         return self.union(other)
 273
 274     def difference(self, other):
 275         """
 276         Return the difference of two sets as a new set.
 277         """
 278         symbols = self._xsymbols([self, other])
 279         islset1 = self._toislset(self.polyhedra, symbols)
 280         islset2 = other._toislset(other.polyhedra, symbols)
 281         islset = libisl.isl_set_subtract(islset1, islset2)
 282         return self._fromislset(islset, symbols)
 283
 284     def __sub__(self, other):
 285         """
 286         Return the difference of two sets as a new set.
 287         """
 288         return self.difference(other)
 289
 290     def lexmin(self):
 291         """
 292         Return a new set containing the lexicographic minimum of the elements in the set.
 293         """
 294         islset = self._toislset(self.polyhedra, self.symbols)
 295         islset = libisl.isl_set_lexmin(islset)
 296         return self._fromislset(islset, self.symbols)
 297
 298     def lexmax(self):
 299         """
 300         Return a new set containing the lexicographic maximum of the elements in the set.
 301         """
 302         islset = self._toislset(self.polyhedra, self.symbols)
 303         islset = libisl.isl_set_lexmax(islset)
 304         return self._fromislset(islset, self.symbols)
 305
 306     def num_parameters(self):
 307         """
 308         Return the total number of parameters, input, output or set dimensions.
 309         """
 310         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 311         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 312         return num
 313
 314     def involves_dims(self, dims):
 315         """
 316         Returns true if set depends on given dimensions.
 317         """
 318         islset = self._toislset(self.polyhedra, self.symbols)
 319         dims = sorted(dims)
 320         symbols = sorted(list(self.symbols))
 321         n = 0
 322         if len(dims)>0:
 323             for dim in dims:
 324                 if dim in symbols:
 325                     first = symbols.index(dims[0])
 326                     n +=1
 327                 else:
 328                     first = 0
 329         else:
 330             return False
 331         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 332         libisl.isl_set_free(islset)
 333         return value
 334
 335     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 336
 337     def vertices(self):
 338         """
 339         Return a list of vertices for this Polygon.
 340         """
 341         from .polyhedra import Polyhedron
 342         if not self.isbounded():
 343             raise ValueError('domain must be bounded')
 344         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 345         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 346         vertices = islhelper.isl_vertices_vertices(vertices)
 347         points = []
 348         for vertex in vertices:
 349             expr = libisl.isl_vertex_get_expr(vertex)
 350             coordinates = []
 351             if islhelper.isl_version < '0.13':
 352                 constraints = islhelper.isl_basic_set_constraints(expr)
 353                 for constraint in constraints:
 354                     constant = libisl.isl_constraint_get_constant_val(constraint)
 355                     constant = islhelper.isl_val_to_int(constant)
 356                     for index, symbol in enumerate(self.symbols):
 357                         coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
 358                             libisl.isl_dim_set, index)
 359                         coefficient = islhelper.isl_val_to_int(coefficient)
 360                         if coefficient != 0:
 361                             coordinate = -Fraction(constant, coefficient)
 362                             coordinates.append((symbol, coordinate))
 363             else:
 364
 365                 # horrible hack, find a cleaner solution
 366                 string = islhelper.isl_multi_aff_to_str(expr)
 367                 matches = self._RE_COORDINATE.finditer(string)
 368                 for symbol, match in zip(self.symbols, matches):
 369                     numerator = int(match.group('num'))
 370                     denominator = match.group('den')
 371                     denominator = 1 if denominator is None else int(denominator)
 372                     coordinate = Fraction(numerator, denominator)
 373                     coordinates.append((symbol, coordinate))
 374             points.append(Point(coordinates))
 375         return points
 376
 377     def points(self):
 378         """
 379         Returns the points contained in the set.
 380         """
 381         if not self.isbounded():
 382             raise ValueError('domain must be bounded')
 383         from .polyhedra import Universe, Eq
 384         islset = self._toislset(self.polyhedra, self.symbols)
 385         islpoints = islhelper.isl_set_points(islset)
 386         points = []
 387         for islpoint in islpoints:
 388             coordinates = {}
 389             for index, symbol in enumerate(self.symbols):
 390                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 391                     libisl.isl_dim_set, index)
 392                 coordinate = islhelper.isl_val_to_int(coordinate)
 393                 coordinates[symbol] = coordinate
 394             points.append(Point(coordinates))
 395         return points
 396
 397     def __contains__(self, point):
 398         for polyhedron in self.polyhedra:
 399             if point in polyhedron:
 400                 return True
 401         return False
 402
 403     def subs(self, symbol, expression=None):
 404         polyhedra = [polyhedron.subs(symbol, expression)
 405             for polyhedron in self.polyhedra]
 406         return Domain(*polyhedra)
 407
 408     @classmethod
 409     def _fromislset(cls, islset, symbols):
 410         from .polyhedra import Polyhedron
 411         islset = libisl.isl_set_remove_divs(islset)
 412         islbsets = islhelper.isl_set_basic_sets(islset)
 413         libisl.isl_set_free(islset)
 414         polyhedra = []
 415         for islbset in islbsets:
 416             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 417             polyhedra.append(polyhedron)
 418         if len(polyhedra) == 0:
 419             from .polyhedra import Empty
 420             return Empty
 421         elif len(polyhedra) == 1:
 422             return polyhedra[0]
 423         else:
 424             self = object().__new__(Domain)
 425             self._polyhedra = tuple(polyhedra)
 426             self._symbols = cls._xsymbols(polyhedra)
 427             self._dimension = len(self._symbols)
 428             return self
 429
 430     @classmethod
 431     def _toislset(cls, polyhedra, symbols):
 432         polyhedron = polyhedra[0]
 433         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 434             polyhedron.inequalities, symbols)
 435         islset1 = libisl.isl_set_from_basic_set(islbset)
 436         for polyhedron in polyhedra[1:]:
 437             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 438                 polyhedron.inequalities, symbols)
 439             islset2 = libisl.isl_set_from_basic_set(islbset)
 440             islset1 = libisl.isl_set_union(islset1, islset2)
 441         return islset1
 442
 443     @classmethod
 444     def _fromast(cls, node):
 445         from .polyhedra import Polyhedron
 446         if isinstance(node, ast.Module) and len(node.body) == 1:
 447             return cls._fromast(node.body[0])
 448         elif isinstance(node, ast.Expr):
 449             return cls._fromast(node.value)
 450         elif isinstance(node, ast.UnaryOp):
 451             domain = cls._fromast(node.operand)
 452             if isinstance(node.operand, ast.invert):
 453                 return Not(domain)
 454         elif isinstance(node, ast.BinOp):
 455             domain1 = cls._fromast(node.left)
 456             domain2 = cls._fromast(node.right)
 457             if isinstance(node.op, ast.BitAnd):
 458                 return And(domain1, domain2)
 459             elif isinstance(node.op, ast.BitOr):
 460                 return Or(domain1, domain2)
 461         elif isinstance(node, ast.Compare):
 462             equalities = []
 463             inequalities = []
 464             left = Expression._fromast(node.left)
 465             for i in range(len(node.ops)):
 466                 op = node.ops[i]
 467                 right = Expression._fromast(node.comparators[i])
 468                 if isinstance(op, ast.Lt):
 469                     inequalities.append(right - left - 1)
 470                 elif isinstance(op, ast.LtE):
 471                     inequalities.append(right - left)
 472                 elif isinstance(op, ast.Eq):
 473                     equalities.append(left - right)
 474                 elif isinstance(op, ast.GtE):
 475                     inequalities.append(left - right)
 476                 elif isinstance(op, ast.Gt):
 477                     inequalities.append(left - right - 1)
 478                 else:
 479                     break
 480                 left = right
 481             else:
 482                 return Polyhedron(equalities, inequalities)
 483         raise SyntaxError('invalid syntax')
 484
 485     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 486     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 487     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 488     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 489     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 490     _RE_NUM_VAR = Expression._RE_NUM_VAR
 491     _RE_OPERATORS = re.compile(r'(&|\||~)')
 492
 493     @classmethod
 494     def fromstring(cls, string):
 495         # remove curly brackets
 496         string = cls._RE_BRACES.sub(r'', string)
 497         # replace '=' by '=='
 498         string = cls._RE_EQ.sub(r'\1==\2', string)
 499         # replace 'and', 'or', 'not'
 500         string = cls._RE_AND.sub(r' & ', string)
 501         string = cls._RE_OR.sub(r' | ', string)
 502         string = cls._RE_NOT.sub(r' ~', string)
 503         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 504         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 505         # add parentheses to force precedence
 506         tokens = cls._RE_OPERATORS.split(string)
 507         for i, token in enumerate(tokens):
 508             if i % 2 == 0:
 509                 token = '({})'.format(token)
 510                 tokens[i] = token
 511         string = ''.join(tokens)
 512         tree = ast.parse(string, 'eval')
 513         return cls._fromast(tree)
 514
 515     def __repr__(self):
 516         assert len(self.polyhedra) >= 2
 517         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 518         return 'Or({})'.format(', '.join(strings))
 519
 520     def _repr_latex_(self):
 521         strings = []
 522         for polyhedron in self.polyhedra:
 523             strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
 524         return '${}$'.format(' \\vee '.join(strings))
 525
 526     @classmethod
 527     def fromsympy(cls, expr):
 528         import sympy
 529         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 530         funcmap = {
 531             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 532             sympy.Lt: Lt, sympy.Le: Le,
 533             sympy.Eq: Eq, sympy.Ne: Ne,
 534             sympy.Ge: Ge, sympy.Gt: Gt,
 535         }
 536         if expr.func in funcmap:
 537             args = [Domain.fromsympy(arg) for arg in expr.args]
 538             return funcmap[expr.func](*args)
 539         elif isinstance(expr, sympy.Expr):
 540             return Expression.fromsympy(expr)
 541         raise ValueError('non-domain expression: {!r}'.format(expr))
 542
 543     def tosympy(self):
 544         import sympy
 545         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 546         return sympy.Or(*polyhedra)
 547
 548
 549 def And(*domains):
 550     """
 551     Return the intersection of two sets as a new set.
 552     """
 553     if len(domains) == 0:
 554         from .polyhedra import Universe
 555         return Universe
 556     else:
 557         return domains[0].intersection(*domains[1:])
 558
 559 def Or(*domains):
 560     """
 561     Return the union of sets as a new set.
 562     """
 563     if len(domains) == 0:
 564         from .polyhedra import Empty
 565         return Empty
 566     else:
 567         return domains[0].union(*domains[1:])
 568
 569 def Not(domain):
 570     """
 571     Returns the complement of this set.
 572     """
 573     return ~domain