X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/7b93cea1daf2889e9ee10ca9c22a1b5124404937..ba15f3f33f837b1291f74bc94081e99b860d3228:/linpy/polyhedra.py diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py index e9226f2..b486be1 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 @@ -35,6 +35,11 @@ __all__ = [ class Polyhedron(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', @@ -45,6 +50,36 @@ class Polyhedron(Domain): ) def __new__(cls, equalities=None, inequalities=None): + """ + 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') @@ -57,14 +92,14 @@ class Polyhedron(Domain): equalities = [] else: for i, equality in enumerate(equalities): - if not isinstance(equality, Expression): + 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): + if not isinstance(inequality, LinExpr): raise TypeError('inequalities must be linear expressions') inequalities[i] = inequality.scaleint() symbols = cls._xsymbols(equalities + inequalities) @@ -74,21 +109,24 @@ class Polyhedron(Domain): @property def equalities(self): """ - Return a list of the equalities in a set. + 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 set. + 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 ta list of the constraints of a set. + The tuple of constraints, i.e., equalities and inequalities. This is + semantically equivalent to: equalities + inequalities. """ return self._constraints @@ -96,16 +134,10 @@ class Polyhedron(Domain): def polyhedra(self): return self, - def disjoint(self): - """ - Return a set as disjoint. - """ + def make_disjoint(self): return self def isuniverse(self): - """ - Return true if a set is the Universe set. - """ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols) universe = bool(libisl.isl_basic_set_is_universe(islbset)) @@ -113,9 +145,6 @@ class Polyhedron(Domain): return universe def aspolyhedron(self): - """ - Return polyhedral hull of a set. - """ return self def __contains__(self, point): @@ -132,10 +161,6 @@ 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) @@ -149,6 +174,9 @@ class Polyhedron(Domain): return inequalities def widen(self, other): + """ + Compute the standard widening of two polyhedra, à la Halbwachs. + """ if not isinstance(other, Polyhedron): raise ValueError('argument must be a Polyhedron instance') inequalities1 = self._asinequalities() @@ -182,7 +210,7 @@ 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: @@ -249,7 +277,6 @@ class Polyhedron(Domain): else: return 'And({})'.format(', '.join(strings)) - def _repr_latex_(self): strings = [] for equality in self.equalities: @@ -260,18 +287,12 @@ class Polyhedron(Domain): @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: @@ -282,6 +303,9 @@ class Polyhedron(Domain): class EmptyType(Polyhedron): + """ + The empty polyhedron, whose set of constraints is not satisfiable. + """ __slots__ = Polyhedron.__slots__ @@ -309,6 +333,10 @@ Empty = EmptyType() class UniverseType(Polyhedron): + """ + The universe polyhedron, whose set of constraints is always satisfiable, + i.e. is empty. + """ __slots__ = Polyhedron.__slots__ @@ -333,13 +361,13 @@ 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: @@ -351,41 +379,42 @@ def _polymorphic(func): @_polymorphic def Lt(left, right): """ - Assert first set is less than the second set. + Create the polyhedron with constraints expr1 < expr2 < expr3 ... """ return Polyhedron([], [right - left - 1]) @_polymorphic def Le(left, right): """ - Assert first set is less than or equal to the second set. + Create the polyhedron with constraints expr1 <= expr2 <= expr3 ... """ return Polyhedron([], [right - left]) @_polymorphic def Eq(left, right): """ - Assert first set is equal to the second set. + Create the polyhedron with constraints expr1 == expr2 == expr3 ... """ return Polyhedron([left - right], []) @_polymorphic def Ne(left, right): """ - Assert first set is not equal to the second set. + 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): """ - Assert first set is greater than the second set. + Create the polyhedron with constraints expr1 > expr2 > expr3 ... """ return Polyhedron([], [left - right - 1]) @_polymorphic def Ge(left, right): """ - Assert first set is greater than or equal to the second set. + Create the polyhedron with constraints expr1 >= expr2 >= expr3 ... """ return Polyhedron([], [left - right])