1 import functools
2 import numbers
4 from . import islhelper
6 from .islhelper import mainctx, libisl
7 from .linexprs import Expression, Rational
8 from .domains import Domain
11 __all__ = [
12 'Polyhedron',
13 'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
14 'Empty', 'Universe',
15 ]
18 class Polyhedron(Domain):
20 __slots__ = (
21 '_equalities',
22 '_inequalities',
23 '_constraints',
24 '_symbols',
25 '_dimension',
26 )
28 def __new__(cls, equalities=None, inequalities=None):
29 if isinstance(equalities, str):
30 if inequalities is not None:
31 raise TypeError('too many arguments')
32 return cls.fromstring(equalities)
33 elif isinstance(equalities, Polyhedron):
34 if inequalities is not None:
35 raise TypeError('too many arguments')
36 return equalities
37 elif isinstance(equalities, Domain):
38 if inequalities is not None:
39 raise TypeError('too many arguments')
40 return equalities.polyhedral_hull()
41 if equalities is None:
42 equalities = []
43 else:
44 for i, equality in enumerate(equalities):
45 if not isinstance(equality, Expression):
46 raise TypeError('equalities must be linear expressions')
47 equalities[i] = equality.scaleint()
48 if inequalities is None:
49 inequalities = []
50 else:
51 for i, inequality in enumerate(inequalities):
52 if not isinstance(inequality, Expression):
53 raise TypeError('inequalities must be linear expressions')
54 inequalities[i] = inequality.scaleint()
55 symbols = cls._xsymbols(equalities + inequalities)
56 islbset = cls._toislbasicset(equalities, inequalities, symbols)
57 return cls._fromislbasicset(islbset, symbols)
59 @property
60 def equalities(self):
61 return self._equalities
63 @property
64 def inequalities(self):
65 return self._inequalities
67 @property
68 def constraints(self):
69 return self._constraints
71 @property
72 def polyhedra(self):
73 return self,
75 def disjoint(self):
76 return self
78 def isuniverse(self):
79 islbset = self._toislbasicset(self.equalities, self.inequalities,
80 self.symbols)
81 universe = bool(libisl.isl_basic_set_is_universe(islbset))
82 libisl.isl_basic_set_free(islbset)
83 return universe
85 def polyhedral_hull(self):
86 return self
88 @classmethod
89 def _fromislbasicset(cls, islbset, symbols):
90 islconstraints = islhelper.isl_basic_set_constraints(islbset)
91 equalities = []
92 inequalities = []
93 for islconstraint in islconstraints:
94 constant = libisl.isl_constraint_get_constant_val(islconstraint)
95 constant = islhelper.isl_val_to_int(constant)
96 coefficients = {}
97 for index, symbol in enumerate(symbols):
98 coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
99 libisl.isl_dim_set, index)
100 coefficient = islhelper.isl_val_to_int(coefficient)
101 if coefficient != 0:
102 coefficients[symbol] = coefficient
103 expression = Expression(coefficients, constant)
104 if libisl.isl_constraint_is_equality(islconstraint):
105 equalities.append(expression)
106 else:
107 inequalities.append(expression)
108 libisl.isl_basic_set_free(islbset)
109 self = object().__new__(Polyhedron)
110 self._equalities = tuple(equalities)
111 self._inequalities = tuple(inequalities)
112 self._constraints = tuple(equalities + inequalities)
113 self._symbols = cls._xsymbols(self._constraints)
114 self._dimension = len(self._symbols)
115 return self
117 @classmethod
118 def _toislbasicset(cls, equalities, inequalities, symbols):
119 dimension = len(symbols)
120 indices = {symbol: index for index, symbol in enumerate(symbols)}
121 islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
122 islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
123 islls = libisl.isl_local_space_from_space(islsp)
124 for equality in equalities:
125 isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
126 for symbol, coefficient in equality.coefficients():
127 islval = str(coefficient).encode()
128 islval = libisl.isl_val_read_from_str(mainctx, islval)
129 index = indices[symbol]
130 isleq = libisl.isl_constraint_set_coefficient_val(isleq,
131 libisl.isl_dim_set, index, islval)
132 if equality.constant != 0:
133 islval = str(equality.constant).encode()
134 islval = libisl.isl_val_read_from_str(mainctx, islval)
135 isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
136 islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
137 for inequality in inequalities:
138 islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
139 for symbol, coefficient in inequality.coefficients():
140 islval = str(coefficient).encode()
141 islval = libisl.isl_val_read_from_str(mainctx, islval)
142 index = indices[symbol]
143 islin = libisl.isl_constraint_set_coefficient_val(islin,
144 libisl.isl_dim_set, index, islval)
145 if inequality.constant != 0:
146 islval = str(inequality.constant).encode()
147 islval = libisl.isl_val_read_from_str(mainctx, islval)
148 islin = libisl.isl_constraint_set_constant_val(islin, islval)
149 islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
150 return islbset
152 @classmethod
153 def fromstring(cls, string):
154 domain = Domain.fromstring(string)
155 if not isinstance(domain, Polyhedron):
156 raise ValueError('non-polyhedral expression: {!r}'.format(string))
157 return domain
159 def __repr__(self):
160 if self.isempty():
161 return 'Empty'
162 elif self.isuniverse():
163 return 'Universe'
164 else:
165 strings = []
166 for equality in self.equalities:
167 strings.append('Eq({}, 0)'.format(equality))
168 for inequality in self.inequalities:
169 strings.append('Ge({}, 0)'.format(inequality))
170 if len(strings) == 1:
171 return strings[0]
172 else:
173 return 'And({})'.format(', '.join(strings))
175 @classmethod
176 def _fromsympy(cls, expr):
177 import sympy
178 equalities = []
179 inequalities = []
180 if expr.func == sympy.And:
181 for arg in expr.args:
182 arg_eqs, arg_ins = cls._fromsympy(arg)
183 equalities.extend(arg_eqs)
184 inequalities.extend(arg_ins)
185 elif expr.func == sympy.Eq:
186 expr = Expression.fromsympy(expr.args[0] - expr.args[1])
187 equalities.append(expr)
188 else:
189 if expr.func == sympy.Lt:
190 expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
191 elif expr.func == sympy.Le:
192 expr = Expression.fromsympy(expr.args[1] - expr.args[0])
193 elif expr.func == sympy.Ge:
194 expr = Expression.fromsympy(expr.args[0] - expr.args[1])
195 elif expr.func == sympy.Gt:
196 expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
197 else:
198 raise ValueError('non-polyhedral expression: {!r}'.format(expr))
199 inequalities.append(expr)
200 return equalities, inequalities
202 @classmethod
203 def fromsympy(cls, expr):
204 import sympy
205 equalities, inequalities = cls._fromsympy(expr)
206 return cls(equalities, inequalities)
208 def tosympy(self):
209 import sympy
210 constraints = []
211 for equality in self.equalities:
212 constraints.append(sympy.Eq(equality.tosympy(), 0))
213 for inequality in self.inequalities:
214 constraints.append(sympy.Ge(inequality.tosympy(), 0))
215 return sympy.And(*constraints)
218 def _polymorphic(func):
219 @functools.wraps(func)
220 def wrapper(left, right):
221 if isinstance(left, numbers.Rational):
222 left = Rational(left)
223 elif not isinstance(left, Expression):
224 raise TypeError('left must be a a rational number '
225 'or a linear expression')
226 if isinstance(right, numbers.Rational):
227 right = Rational(right)
228 elif not isinstance(right, Expression):
229 raise TypeError('right must be a a rational number '
230 'or a linear expression')
231 return func(left, right)
232 return wrapper
234 @_polymorphic
235 def Lt(left, right):
236 return Polyhedron([], [right - left - 1])
238 @_polymorphic
239 def Le(left, right):
240 return Polyhedron([], [right - left])
242 @_polymorphic
243 def Eq(left, right):
244 return Polyhedron([left - right], [])
246 @_polymorphic
247 def Ne(left, right):
248 return ~Eq(left, right)
250 @_polymorphic
251 def Gt(left, right):
252 return Polyhedron([], [left - right - 1])
254 @_polymorphic
255 def Ge(left, right):
256 return Polyhedron([], [left - right])
259 Empty = Eq(1, 0)
261 Universe = Polyhedron([])