2ef0d2a1f2e2065073172dd3e3f46af6f6e14de8
[linpy.git] / pypol / linear.py
1 import functools
2 import numbers
3 import ctypes, ctypes.util
4 from pypol import isl
5
6 from fractions import Fraction, gcd
7
8 libisl = ctypes.CDLL(ctypes.util.find_library('isl'))
9
10 libisl.isl_printer_get_str.restype = ctypes.c_char_p
11
12 __all__ = [
13 'Expression',
14 'constant', 'symbol', 'symbols',
15 'eq', 'le', 'lt', 'ge', 'gt',
16 'Polyhedron',
17 'empty', 'universe'
18 ]
19
20
21 _CONTEXT = isl.Context()
22
23 def _polymorphic_method(func):
24 @functools.wraps(func)
25 def wrapper(a, b):
26 if isinstance(b, Expression):
27 return func(a, b)
28 if isinstance(b, numbers.Rational):
29 b = constant(b)
30 return func(a, b)
31 return NotImplemented
32 return wrapper
33
34 def _polymorphic_operator(func):
35 # A polymorphic operator should call a polymorphic method, hence we just
36 # have to test the left operand.
37 @functools.wraps(func)
38 def wrapper(a, b):
39 if isinstance(a, numbers.Rational):
40 a = constant(a)
41 return func(a, b)
42 elif isinstance(a, Expression):
43 return func(a, b)
44 raise TypeError('arguments must be linear expressions')
45 return wrapper
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 return self
76
77
78 def symbols(self):
79 yield from sorted(self._coefficients)
80
81 @property
82 def dimension(self):
83 return len(list(self.symbols()))
84
85 def coefficient(self, symbol):
86 if isinstance(symbol, Expression) and symbol.issymbol():
87 symbol = str(symbol)
88 elif not isinstance(symbol, str):
89 raise TypeError('symbol must be a string')
90 try:
91 return self._coefficients[symbol]
92 except KeyError:
93 return 0
94
95 __getitem__ = coefficient
96
97 def coefficients(self):
98 for symbol in self.symbols():
99 yield symbol, self.coefficient(symbol)
100
101 @property
102 def constant(self):
103 return self._constant
104
105 def isconstant(self):
106 return len(self._coefficients) == 0
107
108 def values(self):
109 for symbol in self.symbols():
110 yield self.coefficient(symbol)
111 yield self.constant
112
113 def values_int(self):
114 for symbol in self.symbols():
115 return self.coefficient(symbol)
116 return int(self.constant)
117
118
119 def symbol(self):
120 if not self.issymbol():
121 raise ValueError('not a symbol: {}'.format(self))
122 for symbol in self.symbols():
123 return symbol
124
125 def issymbol(self):
126 return len(self._coefficients) == 1 and self._constant == 0
127
128 def __bool__(self):
129 return (not self.isconstant()) or bool(self.constant)
130
131 def __pos__(self):
132 return self
133
134 def __neg__(self):
135 return self * -1
136
137 @_polymorphic_method
138 def __add__(self, other):
139 coefficients = dict(self.coefficients())
140 for symbol, coefficient in other.coefficients():
141 if symbol in coefficients:
142 coefficients[symbol] += coefficient
143 else:
144 coefficients[symbol] = coefficient
145 constant = self.constant + other.constant
146 return Expression(coefficients, constant)
147
148 __radd__ = __add__
149
150 @_polymorphic_method
151 def __sub__(self, other):
152 coefficients = dict(self.coefficients())
153 for symbol, coefficient in other.coefficients():
154 if symbol in coefficients:
155 coefficients[symbol] -= coefficient
156 else:
157 coefficients[symbol] = -coefficient
158 constant = self.constant - other.constant
159 return Expression(coefficients, constant)
160
161 def __rsub__(self, other):
162 return -(self - other)
163
164 @_polymorphic_method
165 def __mul__(self, other):
166 if other.isconstant():
167 coefficients = dict(self.coefficients())
168 for symbol in coefficients:
169 coefficients[symbol] *= other.constant
170 constant = self.constant * other.constant
171 return Expression(coefficients, constant)
172 if isinstance(other, Expression) and not self.isconstant():
173 raise ValueError('non-linear expression: '
174 '{} * {}'.format(self._parenstr(), other._parenstr()))
175 return NotImplemented
176
177 __rmul__ = __mul__
178
179 @_polymorphic_method
180 def __truediv__(self, other):
181 if other.isconstant():
182 coefficients = dict(self.coefficients())
183 for symbol in coefficients:
184 coefficients[symbol] = \
185 Fraction(coefficients[symbol], other.constant)
186 constant = Fraction(self.constant, other.constant)
187 return Expression(coefficients, constant)
188 if isinstance(other, Expression):
189 raise ValueError('non-linear expression: '
190 '{} / {}'.format(self._parenstr(), other._parenstr()))
191 return NotImplemented
192
193 def __rtruediv__(self, other):
194 if isinstance(other, self):
195 if self.isconstant():
196 constant = Fraction(other, self.constant)
197 return Expression(constant=constant)
198 else:
199 raise ValueError('non-linear expression: '
200 '{} / {}'.format(other._parenstr(), self._parenstr()))
201 return NotImplemented
202
203 def __str__(self):
204 string = ''
205 symbols = sorted(self.symbols())
206 i = 0
207 for symbol in symbols:
208 coefficient = self[symbol]
209 if coefficient == 1:
210 if i == 0:
211 string += symbol
212 else:
213 string += ' + {}'.format(symbol)
214 elif coefficient == -1:
215 if i == 0:
216 string += '-{}'.format(symbol)
217 else:
218 string += ' - {}'.format(symbol)
219 else:
220 if i == 0:
221 string += '{}*{}'.format(coefficient, symbol)
222 elif coefficient > 0:
223 string += ' + {}*{}'.format(coefficient, symbol)
224 else:
225 assert coefficient < 0
226 coefficient *= -1
227 string += ' - {}*{}'.format(coefficient, symbol)
228 i += 1
229 constant = self.constant
230 if constant != 0 and i == 0:
231 string += '{}'.format(constant)
232 elif constant > 0:
233 string += ' + {}'.format(constant)
234 elif constant < 0:
235 constant *= -1
236 string += ' - {}'.format(constant)
237 if string == '':
238 string = '0'
239 return string
240
241 def _parenstr(self, always=False):
242 string = str(self)
243 if not always and (self.isconstant() or self.issymbol()):
244 return string
245 else:
246 return '({})'.format(string)
247
248 def __repr__(self):
249 string = '{}({{'.format(self.__class__.__name__)
250 for i, (symbol, coefficient) in enumerate(self.coefficients()):
251 if i != 0:
252 string += ', '
253 string += '{!r}: {!r}'.format(symbol, coefficient)
254 string += '}}, {!r})'.format(self.constant)
255 return string
256
257 @classmethod
258 def fromstring(cls, string):
259 raise NotImplementedError
260
261 @_polymorphic_method
262 def __eq__(self, other):
263 # "normal" equality
264 # see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
265 return isinstance(other, Expression) and \
266 self._coefficients == other._coefficients and \
267 self.constant == other.constant
268
269 def __hash__(self):
270 return hash((self._coefficients, self._constant))
271
272 def _canonify(self):
273 lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
274 [value.denominator for value in self.values()])
275 return self * lcm
276
277 @_polymorphic_method
278 def _eq(self, other):
279 return Polyhedron(equalities=[(self - other)._canonify()])
280
281 @_polymorphic_method
282 def __le__(self, other):
283 return Polyhedron(inequalities=[(self - other)._canonify()])
284
285 @_polymorphic_method
286 def __lt__(self, other):
287 return Polyhedron(inequalities=[(self - other)._canonify() + 1])
288
289 @_polymorphic_method
290 def __ge__(self, other):
291 return Polyhedron(inequalities=[(other - self)._canonify()])
292
293 @_polymorphic_method
294 def __gt__(self, other):
295 return Polyhedron(inequalities=[(other - self)._canonify() + 1])
296
297
298 def constant(numerator=0, denominator=None):
299 if denominator is None and isinstance(numerator, numbers.Rational):
300 return Expression(constant=3)
301 else:
302 return Expression(constant=Fraction(numerator, denominator))
303
304 def symbol(name):
305 if not isinstance(name, str):
306 raise TypeError('name must be a string')
307 return Expression(coefficients={name: 1})
308
309 def symbols(names):
310 if isinstance(names, str):
311 names = names.replace(',', ' ').split()
312 return (symbol(name) for name in names)
313
314
315 @_polymorphic_operator
316 def eq(a, b):
317 return a._eq(b)
318
319 @_polymorphic_operator
320 def le(a, b):
321 return a <= b
322
323 @_polymorphic_operator
324 def lt(a, b):
325 return a < b
326
327 @_polymorphic_operator
328 def ge(a, b):
329 return a >= b
330
331 @_polymorphic_operator
332 def gt(a, b):
333 return a > b
334
335
336 class Polyhedron:
337 """
338 This class implements polyhedrons.
339 """
340
341 def __new__(cls, equalities=None, inequalities=None):
342 if isinstance(equalities, str):
343 if inequalities is not None:
344 raise TypeError('too many arguments')
345 return cls.fromstring(equalities)
346 self = super().__new__(cls)
347 self._equalities = []
348 if equalities is not None:
349 for constraint in equalities:
350 for value in constraint.values():
351 if value.denominator != 1:
352 raise TypeError('non-integer constraint: '
353 '{} == 0'.format(constraint))
354 self._equalities.append(constraint)
355 self._inequalities = []
356 if inequalities is not None:
357 for constraint in inequalities:
358 for value in constraint.values():
359 if value.denominator != 1:
360 raise TypeError('non-integer constraint: '
361 '{} <= 0'.format(constraint))
362 self._inequalities.append(constraint)
363 self._bset = self.to_isl()
364 return self._bset
365
366
367 @property
368 def equalities(self):
369 yield from self._equalities
370
371 @property
372 def inequalities(self):
373 yield from self._inequalities
374
375 @property
376 def constant(self):
377 return self._constant
378
379 def isconstant(self):
380 return len(self._coefficients) == 0
381
382
383 def isempty(self):
384 return bool(libisl.isl_basic_set_is_empty(self._bset))
385
386 def constraints(self):
387 yield from self.equalities
388 yield from self.inequalities
389
390
391 def symbols(self):
392 s = set()
393 for constraint in self.constraints():
394 s.update(constraint.symbols)
395 yield from sorted(s)
396
397 def symbol_count(self):
398 s = []
399 for constraint in self.constraints():
400 s.append(constraint.symbols)
401 return s
402
403 @property
404 def dimension(self):
405 return len(self.symbols())
406
407 def __bool__(self):
408 # return false if the polyhedron is empty, true otherwise
409 if self._equalities or self._inequalities:
410 return False
411 else:
412 return True
413
414
415 def __contains__(self, value):
416 # is the value in the polyhedron?
417 raise NotImplementedError
418
419 def __eq__(self, other):
420 raise NotImplementedError
421
422 def is_empty(self):
423 return
424
425 def isuniverse(self):
426 return self == universe
427
428 def isdisjoint(self, other):
429 # return true if the polyhedron has no elements in common with other
430 raise NotImplementedError
431
432 def issubset(self, other):
433 raise NotImplementedError
434
435 def __le__(self, other):
436 return self.issubset(other)
437
438 def __lt__(self, other):
439 raise NotImplementedError
440
441 def issuperset(self, other):
442 # test whether every element in other is in the polyhedron
443 for value in other:
444 if value == self.constraints():
445 return True
446 else:
447 return False
448 raise NotImplementedError
449
450 def __ge__(self, other):
451 return self.issuperset(other)
452
453 def __gt__(self, other):
454 raise NotImplementedError
455
456 def union(self, *others):
457 # return a new polyhedron with elements from the polyhedron and all
458 # others (convex union)
459 raise NotImplementedError
460
461 def __or__(self, other):
462 return self.union(other)
463
464 def intersection(self, *others):
465 # return a new polyhedron with elements common to the polyhedron and all
466 # others
467 # a poor man's implementation could be:
468 # equalities = list(self.equalities)
469 # inequalities = list(self.inequalities)
470 # for other in others:
471 # equalities.extend(other.equalities)
472 # inequalities.extend(other.inequalities)
473 # return self.__class__(equalities, inequalities)
474 raise NotImplementedError
475
476 def __and__(self, other):
477 return self.intersection(other)
478
479 def difference(self, *others):
480 # return a new polyhedron with elements in the polyhedron that are not
481 # in the others
482 raise NotImplementedError
483
484 def __sub__(self, other):
485 return self.difference(other)
486
487 def __str__(self):
488 constraints = []
489 for constraint in self.equalities:
490 constraints.append('{} == 0'.format(constraint))
491 for constraint in self.inequalities:
492 constraints.append('{} <= 0'.format(constraint))
493 return '{{{}}}'.format(', '.join(constraints))
494
495 def __repr__(self):
496 equalities = list(self.equalities)
497 inequalities = list(self.inequalities)
498 return '{}(equalities={!r}, inequalities={!r})' \
499 ''.format(self.__class__.__name__, equalities, inequalities)
500
501 @classmethod
502 def fromstring(cls, string):
503 raise NotImplementedError
504
505 def to_isl(self):
506 space = libisl.isl_space_set_alloc(_CONTEXT, 0, len(self.symbol_count()))
507 bset = libisl.isl_basic_set_empty(libisl.isl_space_copy(space))
508 ls = libisl.isl_local_space_from_space(libisl.isl_space_copy(space))
509 ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
510 cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
511 d = Expression().__dict__ #write expression values to dictionary in form {'_constant': value, '_coefficients': value}
512 '''
513 if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set
514 need to change the symbols method to a lookup table for the integer value for each letter that could be a symbol
515 '''
516 if self._equalities:
517 if '_constant' in d:
518 value = d.get('_constant')
519 ceq = libisl.isl_constraint_set_constant_si(ceq, value)
520 if '_coefficients' in d:
521 value_co = d.get('_coefficients')
522 if value_co: #if dictionary not empty add coefficient as to constraint
523 ceq = libisl.isl_constraint_set_coefficient_si(ceq, libisl.isl_set_dim, self.symbols(), value_co)
524 bset = libisl.isl_set_add_constraint(bset, ceq)
525
526 if self._inequalities:
527 if '_constant' in d:
528 value = d.get('_constant')
529 cin = libisl.isl_constraint_set_constant_si(cin, value)
530 if '_coefficients' in d:
531 value_co = d.get('_coefficients')
532 if value_co: #if dictionary not empty add coefficient as to constraint
533 cin = libisl.isl_constraint_set_coefficient_si(cin, libisl.isl_set_dim, self.symbols(), value_co)
534 bset = libisl.isl_set_add_constraint(bset, cin)
535 ip = libisl.isl_printer_to_str(_CONTEXT) #create string printer
536 ip = libisl.isl_printer_print_set(ip, bset) #print set to printer
537 string = libisl.isl_printer_get_str(ip) #get string from printer
538 print(string)
539 return bset
540
541 empty = eq(1, 1)
542
543
544 universe = Polyhedron()