pypol/linear.py

   1 import functools
   2 import numbers
   3
   4 from fractions import Fraction, gcd
   5
   6 from pypol import isl
   7 from pypol.isl import libisl
   8
   9
  10 __all__ = [
  11     'Expression', 'Constant', 'Symbol', 'symbols',
  12     'eq', 'le', 'lt', 'ge', 'gt',
  13     'Polyhedron',
  14     'empty', 'universe'
  15 ]
  16
  17
  18 def _polymorphic_method(func):
  19     @functools.wraps(func)
  20     def wrapper(a, b):
  21         if isinstance(b, Expression):
  22             return func(a, b)
  23         if isinstance(b, numbers.Rational):
  24             b = Constant(b)
  25             return func(a, b)
  26         return NotImplemented
  27     return wrapper
  28
  29 def _polymorphic_operator(func):
  30     # A polymorphic operator should call a polymorphic method, hence we just
  31     # have to test the left operand.
  32     @functools.wraps(func)
  33     def wrapper(a, b):
  34         if isinstance(a, numbers.Rational):
  35             a = Constant(a)
  36             return func(a, b)
  37         elif isinstance(a, Expression):
  38             return func(a, b)
  39         raise TypeError('arguments must be linear expressions')
  40     return wrapper
  41
  42
  43 _main_ctx = isl.Context()
  44
  45
  46 class Expression:
  47     """
  48     This class implements linear expressions.
  49     """
  50
  51     def __new__(cls, coefficients=None, constant=0):
  52         if isinstance(coefficients, str):
  53             if constant:
  54                 raise TypeError('too many arguments')
  55             return cls.fromstring(coefficients)
  56         if isinstance(coefficients, dict):
  57             coefficients = coefficients.items()
  58         if coefficients is None:
  59             return Constant(constant)
  60         coefficients = [(symbol, coefficient)
  61                 for symbol, coefficient in coefficients if coefficient != 0]
  62         if len(coefficients) == 0:
  63             return Constant(constant)
  64         elif len(coefficients) == 1 and constant == 0:
  65             symbol, coefficient = coefficients[0]
  66             if coefficient == 1:
  67                 return Symbol(symbol)
  68         self = object().__new__(cls)
  69         self._coefficients = {}
  70         for symbol, coefficient in coefficients:
  71             if isinstance(symbol, Symbol):
  72                 symbol = str(symbol)
  73             elif not isinstance(symbol, str):
  74                 raise TypeError('symbols must be strings or Symbol instances')
  75             if isinstance(coefficient, Constant):
  76                 coefficient = coefficient.constant
  77             if not isinstance(coefficient, numbers.Rational):
  78                 raise TypeError('coefficients must be rational numbers or Constant instances')
  79             self._coefficients[symbol] = coefficient
  80         if isinstance(constant, Constant):
  81             constant = constant.constant
  82         if not isinstance(constant, numbers.Rational):
  83             raise TypeError('constant must be a rational number or a Constant instance')
  84         self._constant = constant
  85         self._symbols = tuple(sorted(self._coefficients))
  86         self._dimension = len(self._symbols)
  87         return self
  88
  89     @classmethod
  90     def fromstring(cls, string):
  91         raise NotImplementedError
  92
  93     @property
  94     def symbols(self):
  95         return self._symbols
  96
  97     @property
  98     def dimension(self):
  99         return self._dimension
 100
 101     def coefficient(self, symbol):
 102         if isinstance(symbol, Symbol):
 103             symbol = str(symbol)
 104         elif not isinstance(symbol, str):
 105             raise TypeError('symbol must be a string or a Symbol instance')
 106         try:
 107             return self._coefficients[symbol]
 108         except KeyError:
 109             return 0
 110
 111     __getitem__ = coefficient
 112
 113     def coefficients(self):
 114         for symbol in self.symbols:
 115             yield symbol, self.coefficient(symbol)
 116
 117     @property
 118     def constant(self):
 119         return self._constant
 120
 121     def isconstant(self):
 122         return False
 123
 124     def values(self):
 125         for symbol in self.symbols:
 126             yield self.coefficient(symbol)
 127         yield self.constant
 128
 129     @property
 130     def symbol(self):
 131         raise ValueError('not a symbol: {}'.format(self))
 132
 133     def issymbol(self):
 134         return False
 135
 136     def __bool__(self):
 137         return True
 138
 139     def __pos__(self):
 140         return self
 141
 142     def __neg__(self):
 143         return self * -1
 144
 145     @_polymorphic_method
 146     def __add__(self, other):
 147         coefficients = dict(self.coefficients())
 148         for symbol, coefficient in other.coefficients():
 149             if symbol in coefficients:
 150                 coefficients[symbol] += coefficient
 151             else:
 152                 coefficients[symbol] = coefficient
 153         constant = self.constant + other.constant
 154         return Expression(coefficients, constant)
 155
 156     __radd__ = __add__
 157
 158     @_polymorphic_method
 159     def __sub__(self, other):
 160         coefficients = dict(self.coefficients())
 161         for symbol, coefficient in other.coefficients():
 162             if symbol in coefficients:
 163                 coefficients[symbol] -= coefficient
 164             else:
 165                 coefficients[symbol] = -coefficient
 166         constant = self.constant - other.constant
 167         return Expression(coefficients, constant)
 168
 169     def __rsub__(self, other):
 170         return -(self - other)
 171
 172     @_polymorphic_method
 173     def __mul__(self, other):
 174         if other.isconstant():
 175             coefficients = dict(self.coefficients())
 176             for symbol in coefficients:
 177                 coefficients[symbol] *= other.constant
 178             constant = self.constant * other.constant
 179             return Expression(coefficients, constant)
 180         if isinstance(other, Expression) and not self.isconstant():
 181             raise ValueError('non-linear expression: '
 182                     '{} * {}'.format(self._parenstr(), other._parenstr()))
 183         return NotImplemented
 184
 185     __rmul__ = __mul__
 186
 187     @_polymorphic_method
 188     def __truediv__(self, other):
 189         if other.isconstant():
 190             coefficients = dict(self.coefficients())
 191             for symbol in coefficients:
 192                 coefficients[symbol] = \
 193                         Fraction(coefficients[symbol], other.constant)
 194             constant = Fraction(self.constant, other.constant)
 195             return Expression(coefficients, constant)
 196         if isinstance(other, Expression):
 197             raise ValueError('non-linear expression: '
 198                 '{} / {}'.format(self._parenstr(), other._parenstr()))
 199         return NotImplemented
 200
 201     def __rtruediv__(self, other):
 202         if isinstance(other, self):
 203             if self.isconstant():
 204                 constant = Fraction(other, self.constant)
 205                 return Expression(constant=constant)
 206             else:
 207                 raise ValueError('non-linear expression: '
 208                         '{} / {}'.format(other._parenstr(), self._parenstr()))
 209         return NotImplemented
 210
 211     def __str__(self):
 212         string = ''
 213         i = 0
 214         for symbol in self.symbols:
 215             coefficient = self.coefficient(symbol)
 216             if coefficient == 1:
 217                 if i == 0:
 218                     string += symbol
 219                 else:
 220                     string += ' + {}'.format(symbol)
 221             elif coefficient == -1:
 222                 if i == 0:
 223                     string += '-{}'.format(symbol)
 224                 else:
 225                     string += ' - {}'.format(symbol)
 226             else:
 227                 if i == 0:
 228                     string += '{}*{}'.format(coefficient, symbol)
 229                 elif coefficient > 0:
 230                     string += ' + {}*{}'.format(coefficient, symbol)
 231                 else:
 232                     assert coefficient < 0
 233                     coefficient *= -1
 234                     string += ' - {}*{}'.format(coefficient, symbol)
 235             i += 1
 236         constant = self.constant
 237         if constant != 0 and i == 0:
 238             string += '{}'.format(constant)
 239         elif constant > 0:
 240             string += ' + {}'.format(constant)
 241         elif constant < 0:
 242             constant *= -1
 243             string += ' - {}'.format(constant)
 244         if string == '':
 245             string = '0'
 246         return string
 247
 248     def _parenstr(self, always=False):
 249         string = str(self)
 250         if not always and (self.isconstant() or self.issymbol()):
 251             return string
 252         else:
 253             return '({})'.format(string)
 254
 255     def __repr__(self):
 256         string = '{}({{'.format(self.__class__.__name__)
 257         for i, (symbol, coefficient) in enumerate(self.coefficients()):
 258             if i != 0:
 259                 string += ', '
 260             string += '{!r}: {!r}'.format(symbol, coefficient)
 261         string += '}}, {!r})'.format(self.constant)
 262         return string
 263
 264     @_polymorphic_method
 265     def __eq__(self, other):
 266         # "normal" equality
 267         # see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
 268         return isinstance(other, Expression) and \
 269                 self._coefficients == other._coefficients and \
 270                 self.constant == other.constant
 271
 272     def __hash__(self):
 273         return hash((tuple(sorted(self._coefficients.items())), self._constant))
 274
 275     def _toint(self):
 276         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
 277                 [value.denominator for value in self.values()])
 278         return self * lcm
 279
 280     @_polymorphic_method
 281     def _eq(self, other):
 282         return Polyhedron(equalities=[(self - other)._toint()])
 283
 284     @_polymorphic_method
 285     def __le__(self, other):
 286         return Polyhedron(inequalities=[(other - self)._toint()])
 287
 288     @_polymorphic_method
 289     def __lt__(self, other):
 290         return Polyhedron(inequalities=[(other - self)._toint() - 1])
 291
 292     @_polymorphic_method
 293     def __ge__(self, other):
 294         return Polyhedron(inequalities=[(self - other)._toint()])
 295
 296     @_polymorphic_method
 297     def __gt__(self, other):
 298         return Polyhedron(inequalities=[(self - other)._toint() - 1])
 299
 300
 301 class Constant(Expression):
 302
 303     def __new__(cls, numerator=0, denominator=None):
 304         self = object().__new__(cls)
 305         if denominator is None:
 306             if isinstance(numerator, numbers.Rational):
 307                 self._constant = numerator
 308             elif isinstance(numerator, Constant):
 309                 self._constant = numerator.constant
 310             else:
 311                 raise TypeError('constant must be a rational number or a Constant instance')
 312         else:
 313             self._constant = Fraction(numerator, denominator)
 314         self._coefficients = {}
 315         self._symbols = ()
 316         self._dimension = 0
 317         return self
 318
 319     def isconstant(self):
 320         return True
 321
 322     def __bool__(self):
 323         return bool(self.constant)
 324
 325     def __repr__(self):
 326         return '{}({!r})'.format(self.__class__.__name__, self._constant)
 327
 328
 329 class Symbol(Expression):
 330
 331     def __new__(cls, name):
 332         if isinstance(name, Symbol):
 333             name = name.symbol
 334         elif not isinstance(name, str):
 335             raise TypeError('name must be a string or a Symbol instance')
 336         self = object().__new__(cls)
 337         self._coefficients = {name: 1}
 338         self._constant = 0
 339         self._symbols = tuple(name)
 340         self._symbol = name
 341         self._dimension = 1
 342         return self
 343
 344     @property
 345     def symbol(self):
 346         return self._symbol
 347
 348     def issymbol(self):
 349         return True
 350
 351     def __repr__(self):
 352         return '{}({!r})'.format(self.__class__.__name__, self._symbol)
 353
 354 def symbols(names):
 355     if isinstance(names, str):
 356         names = names.replace(',', ' ').split()
 357     return (Symbol(name) for name in names)
 358
 359
 360 @_polymorphic_operator
 361 def eq(a, b):
 362     return a.__eq__(b)
 363
 364 @_polymorphic_operator
 365 def le(a, b):
 366     return a.__le__(b)
 367
 368 @_polymorphic_operator
 369 def lt(a, b):
 370     return a.__lt__(b)
 371
 372 @_polymorphic_operator
 373 def ge(a, b):
 374     return a.__ge__(b)
 375
 376 @_polymorphic_operator
 377 def gt(a, b):
 378     return a.__gt__(b)
 379
 380
 381 class Polyhedron:
 382     """
 383     This class implements polyhedrons.
 384     """
 385
 386     def __new__(cls, equalities=None, inequalities=None):
 387         if isinstance(equalities, str):
 388             if inequalities is not None:
 389                 raise TypeError('too many arguments')
 390             return cls.fromstring(equalities)
 391         self = super().__new__(cls)
 392         self._equalities = []
 393         if equalities is not None:
 394             for constraint in equalities:
 395                 for value in constraint.values():
 396                     if value.denominator != 1:
 397                         raise TypeError('non-integer constraint: '
 398                                 '{} == 0'.format(constraint))
 399                 self._equalities.append(constraint)
 400         self._equalities = tuple(self._equalities)
 401         self._inequalities = []
 402         if inequalities is not None:
 403             for constraint in inequalities:
 404                 for value in constraint.values():
 405                     if value.denominator != 1:
 406                         raise TypeError('non-integer constraint: '
 407                                 '{} <= 0'.format(constraint))
 408                 self._inequalities.append(constraint)
 409         self._inequalities = tuple(self._inequalities)
 410         self._constraints = self._equalities + self._inequalities
 411         self._symbols = set()
 412         for constraint in self._constraints:
 413             self.symbols.update(constraint.symbols)
 414         self._symbols = tuple(sorted(self._symbols))
 415         return self
 416
 417     @classmethod
 418     def fromstring(cls, string):
 419         raise NotImplementedError
 420
 421     @property
 422     def equalities(self):
 423         return self._equalities
 424
 425     @property
 426     def inequalities(self):
 427         return self._inequalities
 428
 429     @property
 430     def constraints(self):
 431         return self._constraints
 432
 433     @property
 434     def symbols(self):
 435         return self._symbols
 436
 437     @property
 438     def dimension(self):
 439         return len(self.symbols)
 440
 441     def __bool__(self):
 442         return not self.is_empty()
 443
 444     def __contains__(self, value):
 445         # is the value in the polyhedron?
 446         raise NotImplementedError
 447
 448     def __eq__(self, other):
 449         # works correctly when symbols is not passed
 450         # should be equal if values are the same even if symbols are different
 451         bset = self._toisl()
 452         other = other._toisl()
 453         return bool(libisl.isl_basic_set_plain_is_equal(bset, other))
 454
 455     def isempty(self):
 456         bset = self._toisl()
 457         return bool(libisl.isl_basic_set_is_empty(bset))
 458
 459     def isuniverse(self):
 460         bset = self._toisl()
 461         return bool(libisl.isl_basic_set_is_universe(bset))
 462
 463     def isdisjoint(self, other):
 464         # return true if the polyhedron has no elements in common with other
 465         #symbols = self._symbolunion(other)
 466         bset = self._toisl()
 467         other = other._toisl()
 468         return bool(libisl.isl_set_is_disjoint(bset, other))
 469
 470     def issubset(self, other):
 471         # check if self(bset) is a subset of other
 472         symbols = self._symbolunion(other)
 473         bset = self._toisl(symbols)
 474         other = other._toisl(symbols)
 475         return bool(libisl.isl_set_is_strict_subset(other, bset))
 476
 477     def __le__(self, other):
 478         return self.issubset(other)
 479
 480     def __lt__(self, other):
 481         symbols = self._symbolunion(other)
 482         bset = self._toisl(symbols)
 483         other = other._toisl(symbols)
 484         return bool(libisl.isl_set_is_strict_subset(other, bset))
 485
 486     def issuperset(self, other):
 487         # test whether every element in other is in the polyhedron
 488         raise NotImplementedError
 489
 490     def __ge__(self, other):
 491         return self.issuperset(other)
 492
 493     def __gt__(self, other):
 494         symbols = self._symbolunion(other)
 495         bset = self._toisl(symbols)
 496         other = other._toisl(symbols)
 497         bool(libisl.isl_set_is_strict_subset(other, bset))
 498         raise NotImplementedError
 499
 500     def union(self, *others):
 501         # return a new polyhedron with elements from the polyhedron and all
 502         # others (convex union)
 503         raise NotImplementedError
 504
 505     def __or__(self, other):
 506         return self.union(other)
 507
 508     def intersection(self, *others):
 509         # return a new polyhedron with elements common to the polyhedron and all
 510         # others
 511         # a poor man's implementation could be:
 512         # equalities = list(self.equalities)
 513         # inequalities = list(self.inequalities)
 514         # for other in others:
 515         #     equalities.extend(other.equalities)
 516         #     inequalities.extend(other.inequalities)
 517         # return self.__class__(equalities, inequalities)
 518         raise NotImplementedError
 519
 520     def __and__(self, other):
 521         return self.intersection(other)
 522
 523     def difference(self, other):
 524         # return a new polyhedron with elements in the polyhedron that are not in the other
 525         symbols = self._symbolunion(other)
 526         bset = self._toisl(symbols)
 527         other = other._toisl(symbols)
 528         difference = libisl.isl_set_subtract(bset, other)
 529         return difference
 530
 531
 532     def __sub__(self, other):
 533         return self.difference(other)
 534
 535     def __str__(self):
 536         constraints = []
 537         for constraint in self.equalities:
 538             constraints.append('{} == 0'.format(constraint))
 539         for constraint in self.inequalities:
 540             constraints.append('{} >= 0'.format(constraint))
 541         return '{{{}}}'.format(', '.join(constraints))
 542
 543     def __repr__(self):
 544         equalities = list(self.equalities)
 545         inequalities = list(self.inequalities)
 546         return '{}(equalities={!r}, inequalities={!r})' \
 547                 ''.format(self.__class__.__name__, equalities, inequalities)
 548
 549     def _symbolunion(self, *others):
 550         symbols = set(self.symbols)
 551         for other in others:
 552             symbols.update(other.symbols)
 553         return sorted(symbols)
 554
 555     def _toisl(self, symbols=None):
 556         if symbols is None:
 557             symbols = self.symbols
 558         num_coefficients = len(symbols)
 559         space = libisl.isl_space_set_alloc(_main_ctx, 0, num_coefficients)
 560         bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
 561         ls = libisl.isl_local_space_from_space(space)
 562         #if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set
 563         for eq in self.equalities:
 564             ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
 565             coeff_eq = dict(eq.coefficients())
 566             if eq.constant:
 567                 value = str(eq.constant).encode()
 568                 val = libisl.isl_val_read_from_str(_main_ctx, value)
 569                 ceq = libisl.isl_constraint_set_constant_val(ceq, val)
 570             for eq in coeff_eq:
 571                 number = str(coeff_eq.get(eq)).encode()
 572                 num = libisl.isl_val_read_from_str(_main_ctx, number)
 573                 iden = symbols.index(eq)
 574                 ceq = libisl.isl_constraint_set_coefficient_val(ceq, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
 575             bset = libisl.isl_basic_set_add_constraint(bset, ceq)
 576         for ineq in self.inequalities:
 577             cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
 578             coeff_in = dict(ineq.coefficients())
 579             if ineq.constant:
 580                 value = str(ineq.constant).encode()
 581                 val = libisl.isl_val_read_from_str(_main_ctx, value)
 582                 cin = libisl.isl_constraint_set_constant_val(cin, val)
 583             for ineq in coeff_in:
 584                 number = str(coeff_in.get(ineq)).encode()
 585                 num = libisl.isl_val_read_from_str(_main_ctx, number)
 586                 iden = symbols.index(ineq)
 587                 cin = libisl.isl_constraint_set_coefficient_val(cin, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
 588             bset = libisl.isl_basic_set_add_constraint(bset, cin)
 589         bset = isl.BasicSet(bset)
 590         return bset
 591
 592     @classmethod
 593     def _fromisl(cls, bset):
 594         raise NotImplementedError
 595         equalities = ...
 596         inequalities = ...
 597         return cls(equalities, inequalities)
 598         '''takes basic set  in isl form and puts back into python version of polyhedron
 599         isl example code gives isl form as:
 600             "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
 601             our printer is giving form as:
 602             { [i0, i1] : 2i1 >= -2 - i0 } '''
 603
 604 empty = None #eq(0,1)
 605 universe = None #Polyhedron()
 606
 607 if __name__ == '__main__':
 608     ex1 = Expression(coefficients={'a': 6, 'b': 6}, constant= 3) #this is the expression that does not work (even without adding values)
 609     ex2 = Expression(coefficients={'x': 4, 'y': 2}, constant= 3)
 610     p = Polyhedron(equalities=[ex2])
 611     p2 = Polyhedron(equalities=[ex2])
 612     print(p._toisl()) # checking is values works for toisl