X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/7fff25bf40e4db570565586fb49165d1675002c2..f03bfa8b26b45b0ba2b47c6eadafa7787200a9c9:/linpy/polyhedra.py diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py index 8eddb2d..50af053 100644 --- a/linpy/polyhedra.py +++ b/linpy/polyhedra.py @@ -23,7 +23,7 @@ from . import islhelper from .islhelper import mainctx, libisl from .geometry import GeometricObject, Point -from .linexprs import Expression, Rational +from .linexprs import LinExpr, Rational from .domains import Domain @@ -36,21 +36,49 @@ __all__ = [ class Polyhedron(Domain): """ - Polyhedron class allows users to build and inspect polyherons. Polyhedron inherits from Domain. + A convex polyhedron (or simply "polyhedron") is the space defined by a + system of linear equalities and inequalities. This space can be + unbounded. """ + __slots__ = ( '_equalities', '_inequalities', - '_constraints', '_symbols', '_dimension', ) def __new__(cls, equalities=None, inequalities=None): """ - Create and return a new Polyhedron from a string or list of equalities and inequalities. + Return a polyhedron from two sequences of linear expressions: equalities + is a list of expressions equal to 0, and inequalities is a list of + expressions greater or equal to 0. For example, the polyhedron + 0 <= x <= 2, 0 <= y <= 2 can be constructed with: + + >>> x, y = symbols('x y') + >>> square = Polyhedron([], [x, 2 - x, y, 2 - y]) + + It may be easier to use comparison operators LinExpr.__lt__(), + LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(), + Le(), Eq(), Ge() and Gt(), using one of the following instructions: + + >>> x, y = symbols('x y') + >>> square = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2) + >>> square = Le(0, x, 2) & Le(0, y, 2) + + It is also possible to build a polyhedron from a string. + + >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2') + + Finally, a polyhedron can be constructed from a GeometricObject + instance, calling the GeometricObject.aspolyedron() method. This way, it + is possible to compute the polyhedral hull of a Domain instance, i.e., + the convex hull of two polyhedra: + + >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2') + >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4') + >>> Polyhedron(square | square2) """ - if isinstance(equalities, str): if inequalities is not None: raise TypeError('too many arguments') @@ -59,59 +87,54 @@ class Polyhedron(Domain): if inequalities is not None: raise TypeError('too many arguments') return equalities.aspolyhedron() - if equalities is None: - equalities = [] - else: - for i, equality in enumerate(equalities): - if not isinstance(equality, Expression): + sc_equalities = [] + if equalities is not None: + for equality in equalities: + if not isinstance(equality, LinExpr): raise TypeError('equalities must be linear expressions') - equalities[i] = equality.scaleint() - if inequalities is None: - inequalities = [] - else: - for i, inequality in enumerate(inequalities): - if not isinstance(inequality, Expression): + sc_equalities.append(equality.scaleint()) + sc_inequalities = [] + if inequalities is not None: + for inequality in inequalities: + if not isinstance(inequality, LinExpr): raise TypeError('inequalities must be linear expressions') - inequalities[i] = inequality.scaleint() - symbols = cls._xsymbols(equalities + inequalities) - islbset = cls._toislbasicset(equalities, inequalities, symbols) + sc_inequalities.append(inequality.scaleint()) + symbols = cls._xsymbols(sc_equalities + sc_inequalities) + islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols) return cls._fromislbasicset(islbset, symbols) @property def equalities(self): """ - Return a list of the equalities in a polyhedron. + The tuple of equalities. This is a list of LinExpr instances that are + equal to 0 in the polyhedron. """ return self._equalities @property def inequalities(self): """ - Return a list of the inequalities in a polyhedron. + The tuple of inequalities. This is a list of LinExpr instances that are + greater or equal to 0 in the polyhedron. """ return self._inequalities @property def constraints(self): """ - Return the list of the constraints of a polyhedron. + The tuple of constraints, i.e., equalities and inequalities. This is + semantically equivalent to: equalities + inequalities. """ - return self._constraints + return self._equalities + self._inequalities @property def polyhedra(self): return self, def make_disjoint(self): - """ - Return a polyhedron as disjoint. - """ return self def isuniverse(self): - """ - Return true if a polyhedron is the Universe set. - """ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols) universe = bool(libisl.isl_basic_set_is_universe(islbset)) @@ -119,15 +142,18 @@ class Polyhedron(Domain): return universe def aspolyhedron(self): - """ - Return the polyhedral hull of a polyhedron. - """ return self - def __contains__(self, point): + def convex_union(self, *others): """ - Report whether a polyhedron constains an integer point + Return the convex union of two or more polyhedra. """ + for other in others: + if not isinstance(other, Polyhedron): + raise TypeError('arguments must be Polyhedron instances') + return Polyhedron(self.union(*others)) + + def __contains__(self, point): if not isinstance(point, Point): raise TypeError('point must be a Point instance') if self.symbols != point.symbols: @@ -141,10 +167,6 @@ 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) @@ -158,8 +180,14 @@ class Polyhedron(Domain): return inequalities def widen(self, other): + """ + Compute the standard widening of two polyhedra, Ã  la Halbwachs. + + In its current implementation, this method is slow and should not be + used on large polyhedra. + """ if not isinstance(other, Polyhedron): - raise ValueError('argument must be a Polyhedron instance') + raise TypeError('argument must be a Polyhedron instance') inequalities1 = self._asinequalities() inequalities2 = other._asinequalities() inequalities = [] @@ -191,7 +219,7 @@ class Polyhedron(Domain): coefficient = islhelper.isl_val_to_int(coefficient) if coefficient != 0: coefficients[symbol] = coefficient - expression = Expression(coefficients, constant) + expression = LinExpr(coefficients, constant) if libisl.isl_constraint_is_equality(islconstraint): equalities.append(expression) else: @@ -200,8 +228,7 @@ class Polyhedron(Domain): self = object().__new__(Polyhedron) self._equalities = tuple(equalities) self._inequalities = tuple(inequalities) - self._constraints = tuple(equalities + inequalities) - self._symbols = cls._xsymbols(self._constraints) + self._symbols = cls._xsymbols(self.constraints) self._dimension = len(self._symbols) return self @@ -242,9 +269,6 @@ class Polyhedron(Domain): @classmethod def fromstring(cls, string): - """ - Create and return a Polyhedron from a string. - """ domain = Domain.fromstring(string) if not isinstance(domain, Polyhedron): raise ValueError('non-polyhedral expression: {!r}'.format(string)) @@ -261,7 +285,6 @@ class Polyhedron(Domain): else: return 'And({})'.format(', '.join(strings)) - def _repr_latex_(self): strings = [] for equality in self.equalities: @@ -272,18 +295,12 @@ class Polyhedron(Domain): @classmethod def fromsympy(cls, expr): - """ - Convert a sympy object to a polyhedron. - """ domain = Domain.fromsympy(expr) if not isinstance(domain, Polyhedron): raise ValueError('non-polyhedral expression: {!r}'.format(expr)) return domain def tosympy(self): - """ - Return a polyhedron as a sympy object. - """ import sympy constraints = [] for equality in self.equalities: @@ -294,14 +311,14 @@ class Polyhedron(Domain): class EmptyType(Polyhedron): - - __slots__ = Polyhedron.__slots__ + """ + The empty polyhedron, whose set of constraints is not satisfiable. + """ def __new__(cls): self = object().__new__(cls) self._equalities = (Rational(1),) self._inequalities = () - self._constraints = self._equalities self._symbols = () self._dimension = 0 return self @@ -321,14 +338,15 @@ Empty = EmptyType() class UniverseType(Polyhedron): - - __slots__ = Polyhedron.__slots__ + """ + The universe polyhedron, whose set of constraints is always satisfiable, + i.e. is empty. + """ def __new__(cls): self = object().__new__(cls) self._equalities = () self._inequalities = () - self._constraints = () self._symbols = () self._dimension = () return self @@ -345,13 +363,13 @@ Universe = UniverseType() def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): - if not isinstance(left, Expression): + if not isinstance(left, LinExpr): if isinstance(left, numbers.Rational): left = Rational(left) else: raise TypeError('left must be a a rational number ' 'or a linear expression') - if not isinstance(right, Expression): + if not isinstance(right, LinExpr): if isinstance(right, numbers.Rational): right = Rational(right) else: @@ -363,41 +381,42 @@ def _polymorphic(func): @_polymorphic def Lt(left, right): """ - Returns a Polyhedron instance with a single constraint as left less than right. + Create the polyhedron with constraints expr1 < expr2 < expr3 ... """ return Polyhedron([], [right - left - 1]) @_polymorphic def Le(left, right): """ - Returns a Polyhedron instance with a single constraint as left less than or equal to right. + Create the polyhedron with constraints expr1 <= expr2 <= expr3 ... """ return Polyhedron([], [right - left]) @_polymorphic def Eq(left, right): """ - Returns a Polyhedron instance with a single constraint as left equal to right. + Create the polyhedron with constraints expr1 == expr2 == expr3 ... """ return Polyhedron([left - right], []) @_polymorphic def Ne(left, right): """ - Returns a Polyhedron instance with a single constraint as left not equal to right. + Create the domain such that expr1 != expr2 != expr3 ... The result is a + Domain, not a Polyhedron. """ return ~Eq(left, right) @_polymorphic -def Gt(left, right): +def Ge(left, right): """ - Returns a Polyhedron instance with a single constraint as left greater than right. + Create the polyhedron with constraints expr1 >= expr2 >= expr3 ... """ - return Polyhedron([], [left - right - 1]) + return Polyhedron([], [left - right]) @_polymorphic -def Ge(left, right): +def Gt(left, right): """ - Returns a Polyhedron instance with a single constraint as left greater than or equal to right. + Create the polyhedron with constraints expr1 > expr2 > expr3 ... """ - return Polyhedron([], [left - right]) + return Polyhedron([], [left - right - 1])