pypol/linear.py

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