X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/843dede1d98c459f9761abff5877e0b019fa0155..960f0c252361dfd696359f803aae40a9b13b14a6:/pypol/polyhedra.py diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index a5d9495..9bfc64b 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,3 +1,20 @@ +# Copyright 2014 MINES ParisTech +# +# This file is part of Linpy. +# +# Linpy is free software: you can redistribute it and/or modify +# it under the terms of the GNU General Public License as published by +# the Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# Linpy is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License +# along with Linpy. If not, see . + import functools import math import numbers @@ -56,14 +73,23 @@ class Polyhedron(Domain): @property def equalities(self): + """ + Return a list of the equalities in a set. + """ return self._equalities @property def inequalities(self): + """ + Return a list of the inequalities in a set. + """ return self._inequalities @property def constraints(self): + """ + Return ta list of the constraints of a set. + """ return self._constraints @property @@ -72,13 +98,13 @@ class Polyhedron(Domain): def disjoint(self): """ - Return this set as disjoint. + Return a set as disjoint. """ return self def isuniverse(self): """ - Return true if this set is the Universe set. + Return true if a set is the Universe set. """ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols) @@ -88,7 +114,7 @@ class Polyhedron(Domain): def aspolyhedron(self): """ - Return polyhedral hull of this set. + Return polyhedral hull of a set. """ return self @@ -106,12 +132,41 @@ class Polyhedron(Domain): return True def subs(self, symbol, expression=None): + """ + Subsitute the given value into an expression and return the resulting + expression. + """ equalities = [equality.subs(symbol, expression) for equality in self.equalities] inequalities = [inequality.subs(symbol, expression) for inequality in self.inequalities] return Polyhedron(equalities, inequalities) + def _asinequalities(self): + inequalities = list(self.equalities) + inequalities.extend([-expression for expression in self.equalities]) + inequalities.extend(self.inequalities) + return inequalities + + def widen(self, other): + if not isinstance(other, Polyhedron): + raise ValueError('argument must be a Polyhedron instance') + inequalities1 = self._asinequalities() + inequalities2 = other._asinequalities() + inequalities = [] + for inequality1 in inequalities1: + if other <= Polyhedron(inequalities=[inequality1]): + inequalities.append(inequality1) + for inequality2 in inequalities2: + for i in range(len(inequalities1)): + inequalities3 = inequalities1[:i] + inequalities[i + 1:] + inequalities3.append(inequality2) + polyhedron3 = Polyhedron(inequalities=inequalities3) + if self == polyhedron3: + inequalities.append(inequality2) + break + return Polyhedron(inequalities=inequalities) + @classmethod def _fromislbasicset(cls, islbset, symbols): islconstraints = islhelper.isl_basic_set_constraints(islbset) @@ -184,42 +239,39 @@ class Polyhedron(Domain): return domain def __repr__(self): - if self.isempty(): - return 'Empty' - elif self.isuniverse(): - return 'Universe' + strings = [] + for equality in self.equalities: + strings.append('Eq({}, 0)'.format(equality)) + for inequality in self.inequalities: + strings.append('Ge({}, 0)'.format(inequality)) + if len(strings) == 1: + return strings[0] else: - strings = [] - for equality in self.equalities: - strings.append('Eq({}, 0)'.format(equality)) - for inequality in self.inequalities: - strings.append('Ge({}, 0)'.format(inequality)) - if len(strings) == 1: - return strings[0] - else: - return 'And({})'.format(', '.join(strings)) + return 'And({})'.format(', '.join(strings)) + def _repr_latex_(self): - if self.isempty(): - return '\$\\emptyset\$' - elif self.isuniverse(): - return '\$\\Omega\$' - else: - strings = [] - for equality in self.equalities: - strings.append('{} = 0'.format(equality._repr_latex_().strip('\$'))) - for inequality in self.inequalities: - strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('\$'))) - return '\${}\$'.format(' \\wedge '.join(strings)) + strings = [] + for equality in self.equalities: + strings.append('{} = 0'.format(equality._repr_latex_().strip('\$'))) + for inequality in self.inequalities: + strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('\$'))) + return '\$\${}\$\$'.format(' \\wedge '.join(strings)) @classmethod def fromsympy(cls, expr): + """ + Convert a sympy object to an expression. + """ domain = Domain.fromsympy(expr) if not isinstance(domain, Polyhedron): raise ValueError('non-polyhedral expression: {!r}'.format(expr)) return domain def tosympy(self): + """ + Return an expression as a sympy object. + """ import sympy constraints = [] for equality in self.equalities: @@ -228,6 +280,56 @@ class Polyhedron(Domain): constraints.append(sympy.Ge(inequality.tosympy(), 0)) return sympy.And(*constraints) + +class EmptyType(Polyhedron): + + __slots__ = Polyhedron.__slots__ + + def __new__(cls): + self = object().__new__(cls) + self._equalities = (Rational(1),) + self._inequalities = () + self._constraints = self._equalities + self._symbols = () + self._dimension = 0 + return self + + def widen(self, other): + if not isinstance(other, Polyhedron): + raise ValueError('argument must be a Polyhedron instance') + return other + + def __repr__(self): + return 'Empty' + + def _repr_latex_(self): + return '\$\$\\emptyset\$\$' + +Empty = EmptyType() + + +class UniverseType(Polyhedron): + + __slots__ = Polyhedron.__slots__ + + def __new__(cls): + self = object().__new__(cls) + self._equalities = () + self._inequalities = () + self._constraints = () + self._symbols = () + self._dimension = () + return self + + def __repr__(self): + return 'Universe' + + def _repr_latex_(self): + return '\$\$\\Omega\$\$' + +Universe = UniverseType() + + def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): @@ -249,46 +351,41 @@ def _polymorphic(func): @_polymorphic def Lt(left, right): """ - Return true if the first set is less than the second. + Assert first set is less than the second set. """ return Polyhedron([], [right - left - 1]) @_polymorphic def Le(left, right): """ - Return true the first set is less than or equal to the second. + Assert first set is less than or equal to the second set. """ return Polyhedron([], [right - left]) @_polymorphic def Eq(left, right): """ - Return true if the sets are equal. + Assert first set is equal to the second set. """ return Polyhedron([left - right], []) @_polymorphic def Ne(left, right): """ - Return true if the sets are NOT equal. + Assert first set is not equal to the second set. """ return ~Eq(left, right) @_polymorphic def Gt(left, right): """ - Return true if the first set is greater than the second set. + Assert first set is greater than the second set. """ return Polyhedron([], [left - right - 1]) @_polymorphic def Ge(left, right): """ - Return true if the first set is greater than or equal the second set. + Assert first set is greater than or equal to the second set. """ return Polyhedron([], [left - right]) - - -Empty = Eq(1, 0) - -Universe = Polyhedron([])