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         islset = self._toislset(self.polyhedra, self.symbols)
  71         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  72         return self._fromislset(islset, self.symbols)
  73
  74     def isempty(self):
  75         islset = self._toislset(self.polyhedra, self.symbols)
  76         empty = bool(libisl.isl_set_is_empty(islset))
  77         libisl.isl_set_free(islset)
  78         return empty
  79
  80     def __bool__(self):
  81         return not self.isempty()
  82
  83     def isuniverse(self):
  84         islset = self._toislset(self.polyhedra, self.symbols)
  85         universe = bool(libisl.isl_set_plain_is_universe(islset))
  86         libisl.isl_set_free(islset)
  87         return universe
  88
  89     def isbounded(self):
  90         islset = self._toislset(self.polyhedra, self.symbols)
  91         bounded = bool(libisl.isl_set_is_bounded(islset))
  92         libisl.isl_set_free(islset)
  93         return bounded
  94
  95     def __eq__(self, other):
  96         symbols = self._xsymbols([self, other])
  97         islset1 = self._toislset(self.polyhedra, symbols)
  98         islset2 = other._toislset(other.polyhedra, symbols)
  99         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
 100         libisl.isl_set_free(islset1)
 101         libisl.isl_set_free(islset2)
 102         return equal
 103
 104     def isdisjoint(self, other):
 105         symbols = self._xsymbols([self, other])
 106         islset1 = self._toislset(self.polyhedra, symbols)
 107         islset2 = self._toislset(other.polyhedra, symbols)
 108         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 109         libisl.isl_set_free(islset1)
 110         libisl.isl_set_free(islset2)
 111         return equal
 112
 113     def issubset(self, other):
 114         symbols = self._xsymbols([self, other])
 115         islset1 = self._toislset(self.polyhedra, symbols)
 116         islset2 = self._toislset(other.polyhedra, symbols)
 117         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 118         libisl.isl_set_free(islset1)
 119         libisl.isl_set_free(islset2)
 120         return equal
 121
 122     def __le__(self, other):
 123         return self.issubset(other)
 124
 125     def __lt__(self, other):
 126         symbols = self._xsymbols([self, other])
 127         islset1 = self._toislset(self.polyhedra, symbols)
 128         islset2 = self._toislset(other.polyhedra, symbols)
 129         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 130         libisl.isl_set_free(islset1)
 131         libisl.isl_set_free(islset2)
 132         return equal
 133
 134     def complement(self):
 135         islset = self._toislset(self.polyhedra, self.symbols)
 136         islset = libisl.isl_set_complement(islset)
 137         return self._fromislset(islset, self.symbols)
 138
 139     def __invert__(self):
 140         return self.complement()
 141
 142     def simplify(self):
 143         #does not change anything in any of the examples
 144         #isl seems to do this naturally
 145         islset = self._toislset(self.polyhedra, self.symbols)
 146         islset = libisl.isl_set_remove_redundancies(islset)
 147         return self._fromislset(islset, self.symbols)
 148
 149     def aspolyhedron(self):
 150         # several types of hull are available
 151         # polyhedral seems to be the more appropriate, to be checked
 152         from .polyhedra import Polyhedron
 153         islset = self._toislset(self.polyhedra, self.symbols)
 154         islbset = libisl.isl_set_polyhedral_hull(islset)
 155         return Polyhedron._fromislbasicset(islbset, self.symbols)
 156
 157     def asdomain(self):
 158         return self
 159
 160     def project(self, dims):
 161         # use to remove certain variables
 162         islset = self._toislset(self.polyhedra, self.symbols)
 163         n = 0
 164         for index, symbol in reversed(list(enumerate(self.symbols))):
 165             if symbol in dims:
 166                 n += 1
 167             elif n > 0:
 168                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 169                 n = 0
 170         if n > 0:
 171             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 172         dims = [symbol for symbol in self.symbols if symbol not in dims]
 173         return Domain._fromislset(islset, dims)
 174
 175     def sample(self):
 176         islset = self._toislset(self.polyhedra, self.symbols)
 177         islpoint = libisl.isl_set_sample_point(islset)
 178         if bool(libisl.isl_point_is_void(islpoint)):
 179             libisl.isl_point_free(islpoint)
 180             raise ValueError('domain must be non-empty')
 181         point = {}
 182         for index, symbol in enumerate(self.symbols):
 183             coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 184                 libisl.isl_dim_set, index)
 185             coordinate = islhelper.isl_val_to_int(coordinate)
 186             point[symbol] = coordinate
 187         libisl.isl_point_free(islpoint)
 188         return point
 189
 190     def intersection(self, *others):
 191         if len(others) == 0:
 192             return self
 193         symbols = self._xsymbols((self,) + others)
 194         islset1 = self._toislset(self.polyhedra, symbols)
 195         for other in others:
 196             islset2 = other._toislset(other.polyhedra, symbols)
 197             islset1 = libisl.isl_set_intersect(islset1, islset2)
 198         return self._fromislset(islset1, symbols)
 199
 200     def __and__(self, other):
 201         return self.intersection(other)
 202
 203     def union(self, *others):
 204         if len(others) == 0:
 205             return self
 206         symbols = self._xsymbols((self,) + others)
 207         islset1 = self._toislset(self.polyhedra, symbols)
 208         for other in others:
 209             islset2 = other._toislset(other.polyhedra, symbols)
 210             islset1 = libisl.isl_set_union(islset1, islset2)
 211         return self._fromislset(islset1, symbols)
 212
 213     def __or__(self, other):
 214         return self.union(other)
 215
 216     def __add__(self, other):
 217         return self.union(other)
 218
 219     def difference(self, other):
 220         symbols = self._xsymbols([self, other])
 221         islset1 = self._toislset(self.polyhedra, symbols)
 222         islset2 = other._toislset(other.polyhedra, symbols)
 223         islset = libisl.isl_set_subtract(islset1, islset2)
 224         return self._fromislset(islset, symbols)
 225
 226     def __sub__(self, other):
 227         return self.difference(other)
 228
 229     def lexmin(self):
 230         islset = self._toislset(self.polyhedra, self.symbols)
 231         islset = libisl.isl_set_lexmin(islset)
 232         return self._fromislset(islset, self.symbols)
 233
 234     def lexmax(self):
 235         islset = self._toislset(self.polyhedra, self.symbols)
 236         islset = libisl.isl_set_lexmax(islset)
 237         return self._fromislset(islset, self.symbols)
 238
 239     def num_parameters(self):
 240         #could be useful with large, complicated polyhedrons
 241         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 242         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 243         return num
 244
 245     def involves_dims(self, dims):
 246         #could be useful with large, complicated polyhedrons
 247         islset = self._toislset(self.polyhedra, self.symbols)
 248         dims = sorted(dims)
 249         symbols = sorted(list(self.symbols))
 250         n = 0
 251         if len(dims)>0:
 252             for dim in dims:
 253                 if dim in symbols:
 254                     first = symbols.index(dims[0])
 255                     n +=1
 256                 else:
 257                     first = 0
 258         else:
 259             return False
 260         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 261         libisl.isl_set_free(islset)
 262         return value
 263
 264     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 265
 266     def vertices(self):
 267         #returning list of verticies
 268         from .polyhedra import Polyhedron
 269         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 270         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 271         vertices = islhelper.isl_vertices_vertices(vertices)
 272         points = []
 273         for vertex in vertices:
 274             expr = libisl.isl_vertex_get_expr(vertex)
 275             coordinates = []
 276             if islhelper.isl_version < '0.13':
 277                 constraints = islhelper.isl_basic_set_constraints(expr)
 278                 for constraint in constraints:
 279                     constant = libisl.isl_constraint_get_constant_val(constraint)
 280                     constant = islhelper.isl_val_to_int(constant)
 281                     for index, symbol in enumerate(self.symbols):
 282                         coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
 283                             libisl.isl_dim_set, index)
 284                         coefficient = islhelper.isl_val_to_int(coefficient)
 285                         if coefficient != 0:
 286                             coordinate = -Fraction(constant, coefficient)
 287                             coordinates.append((symbol, coordinate))
 288             else:
 289                 # horrible hack, find a cleaner solution
 290                 string = islhelper.isl_multi_aff_to_str(expr)
 291                 matches = self._RE_COORDINATE.finditer(string)
 292                 for symbol, match in zip(self.symbols, matches):
 293                     numerator = int(match.group('num'))
 294                     denominator = match.group('den')
 295                     denominator = 1 if denominator is None else int(denominator)
 296                     coordinate = Fraction(numerator, denominator)
 297                     coordinates.append((symbol, coordinate))
 298             points.append(Point(coordinates))
 299         return points
 300
 301     def points(self):
 302         if not self.isbounded():
 303             raise ValueError('domain must be bounded')
 304         from .polyhedra import Universe, Eq
 305         islset = self._toislset(self.polyhedra, self.symbols)
 306         islpoints = islhelper.isl_set_points(islset)
 307         points = []
 308         for islpoint in islpoints:
 309             coordinates = {}
 310             for index, symbol in enumerate(self.symbols):
 311                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 312                     libisl.isl_dim_set, index)
 313                 coordinate = islhelper.isl_val_to_int(coordinate)
 314                 coordinates[symbol] = coordinate
 315             points.append(Point(coordinates))
 316         return points
 317
 318     def __contains__(self, point):
 319         for polyhedron in self.polyhedra:
 320             if point in polyhedron:
 321                 return True
 322         return False
 323
 324     def subs(self, symbol, expression=None):
 325         polyhedra = [polyhedron.subs(symbol, expression)
 326             for polyhedron in self.polyhedra]
 327         return Domain(*polyhedra)
 328
 329     @classmethod
 330     def _fromislset(cls, islset, symbols):
 331         from .polyhedra import Polyhedron
 332         islset = libisl.isl_set_remove_divs(islset)
 333         islbsets = islhelper.isl_set_basic_sets(islset)
 334         libisl.isl_set_free(islset)
 335         polyhedra = []
 336         for islbset in islbsets:
 337             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 338             polyhedra.append(polyhedron)
 339         if len(polyhedra) == 0:
 340             from .polyhedra import Empty
 341             return Empty
 342         elif len(polyhedra) == 1:
 343             return polyhedra[0]
 344         else:
 345             self = object().__new__(Domain)
 346             self._polyhedra = tuple(polyhedra)
 347             self._symbols = cls._xsymbols(polyhedra)
 348             self._dimension = len(self._symbols)
 349             return self
 350
 351     @classmethod
 352     def _toislset(cls, polyhedra, symbols):
 353         polyhedron = polyhedra[0]
 354         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 355             polyhedron.inequalities, symbols)
 356         islset1 = libisl.isl_set_from_basic_set(islbset)
 357         for polyhedron in polyhedra[1:]:
 358             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 359                 polyhedron.inequalities, symbols)
 360             islset2 = libisl.isl_set_from_basic_set(islbset)
 361             islset1 = libisl.isl_set_union(islset1, islset2)
 362         return islset1
 363
 364     @classmethod
 365     def _fromast(cls, node):
 366         from .polyhedra import Polyhedron
 367         if isinstance(node, ast.Module) and len(node.body) == 1:
 368             return cls._fromast(node.body[0])
 369         elif isinstance(node, ast.Expr):
 370             return cls._fromast(node.value)
 371         elif isinstance(node, ast.UnaryOp):
 372             domain = cls._fromast(node.operand)
 373             if isinstance(node.operand, ast.invert):
 374                 return Not(domain)
 375         elif isinstance(node, ast.BinOp):
 376             domain1 = cls._fromast(node.left)
 377             domain2 = cls._fromast(node.right)
 378             if isinstance(node.op, ast.BitAnd):
 379                 return And(domain1, domain2)
 380             elif isinstance(node.op, ast.BitOr):
 381                 return Or(domain1, domain2)
 382         elif isinstance(node, ast.Compare):
 383             equalities = []
 384             inequalities = []
 385             left = Expression._fromast(node.left)
 386             for i in range(len(node.ops)):
 387                 op = node.ops[i]
 388                 right = Expression._fromast(node.comparators[i])
 389                 if isinstance(op, ast.Lt):
 390                     inequalities.append(right - left - 1)
 391                 elif isinstance(op, ast.LtE):
 392                     inequalities.append(right - left)
 393                 elif isinstance(op, ast.Eq):
 394                     equalities.append(left - right)
 395                 elif isinstance(op, ast.GtE):
 396                     inequalities.append(left - right)
 397                 elif isinstance(op, ast.Gt):
 398                     inequalities.append(left - right - 1)
 399                 else:
 400                     break
 401                 left = right
 402             else:
 403                 return Polyhedron(equalities, inequalities)
 404         raise SyntaxError('invalid syntax')
 405
 406     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 407     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 408     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 409     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 410     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 411     _RE_NUM_VAR = Expression._RE_NUM_VAR
 412     _RE_OPERATORS = re.compile(r'(&|\||~)')
 413
 414     @classmethod
 415     def fromstring(cls, string):
 416         # remove curly brackets
 417         string = cls._RE_BRACES.sub(r'', string)
 418         # replace '=' by '=='
 419         string = cls._RE_EQ.sub(r'\1==\2', string)
 420         # replace 'and', 'or', 'not'
 421         string = cls._RE_AND.sub(r' & ', string)
 422         string = cls._RE_OR.sub(r' | ', string)
 423         string = cls._RE_NOT.sub(r' ~', string)
 424         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 425         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 426         # add parentheses to force precedence
 427         tokens = cls._RE_OPERATORS.split(string)
 428         for i, token in enumerate(tokens):
 429             if i % 2 == 0:
 430                 token = '({})'.format(token)
 431                 tokens[i] = token
 432         string = ''.join(tokens)
 433         tree = ast.parse(string, 'eval')
 434         return cls._fromast(tree)
 435
 436     def __repr__(self):
 437         assert len(self.polyhedra) >= 2
 438         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 439         return 'Or({})'.format(', '.join(strings))
 440
 441     def _repr_latex_(self):
 442         strings = []
 443         for polyhedron in self.polyhedra:
 444             strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
 445         return '${}$'.format(' \\vee '.join(strings))
 446
 447     @classmethod
 448     def fromsympy(cls, expr):
 449         import sympy
 450         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 451         funcmap = {
 452             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 453             sympy.Lt: Lt, sympy.Le: Le,
 454             sympy.Eq: Eq, sympy.Ne: Ne,
 455             sympy.Ge: Ge, sympy.Gt: Gt,
 456         }
 457         if expr.func in funcmap:
 458             args = [Domain.fromsympy(arg) for arg in expr.args]
 459             return funcmap[expr.func](*args)
 460         elif isinstance(expr, sympy.Expr):
 461             return Expression.fromsympy(expr)
 462         raise ValueError('non-domain expression: {!r}'.format(expr))
 463
 464     def tosympy(self):
 465         import sympy
 466         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 467         return sympy.Or(*polyhedra)
 468
 469
 470 def And(*domains):
 471     if len(domains) == 0:
 472         from .polyhedra import Universe
 473         return Universe
 474     else:
 475         return domains[0].intersection(*domains[1:])
 476
 477 def Or(*domains):
 478     if len(domains) == 0:
 479         from .polyhedra import Empty
 480         return Empty
 481     else:
 482         return domains[0].union(*domains[1:])
 483
 484 def Not(domain):
 485     return ~domain