index ac67cf8..fe143d4 100644 (file)
@@ -1,10 +1,12 @@
import functools
+import math
import numbers

from . import islhelper

from .islhelper import mainctx, libisl
-from .linexprs import Expression, Constant
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational
from .domains import Domain

@@ -30,42 +32,47 @@ class Polyhedron(Domain):
if inequalities is not None:
raise TypeError('too many arguments')
return cls.fromstring(equalities)
-        elif isinstance(equalities, Polyhedron):
+        elif isinstance(equalities, GeometricObject):
if inequalities is not None:
raise TypeError('too many arguments')
-            return equalities
-        elif isinstance(equalities, Domain):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities.polyhedral_hull()
+            return equalities.aspolyhedron()
if equalities is None:
equalities = []
else:
for i, equality in enumerate(equalities):
if not isinstance(equality, Expression):
raise TypeError('equalities must be linear expressions')
-                equalities[i] = equality._toint()
+                equalities[i] = equality.scaleint()
if inequalities is None:
inequalities = []
else:
for i, inequality in enumerate(inequalities):
if not isinstance(inequality, Expression):
raise TypeError('inequalities must be linear expressions')
-                inequalities[i] = inequality._toint()
+                inequalities[i] = inequality.scaleint()
symbols = cls._xsymbols(equalities + inequalities)
islbset = cls._toislbasicset(equalities, inequalities, symbols)
return cls._fromislbasicset(islbset, symbols)

@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
@@ -73,18 +80,75 @@ class Polyhedron(Domain):
return self,

def disjoint(self):
+        """
+        Return a set as disjoint.
+        """
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))
libisl.isl_basic_set_free(islbset)
return universe

-    def polyhedral_hull(self):
+    def aspolyhedron(self):
+        """
+        Return polyhedral hull of a set.
+        """
return self

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        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)
@@ -95,7 +159,8 @@ class Polyhedron(Domain):
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
for index, symbol in enumerate(symbols):
-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, index)
+                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
+                    libisl.isl_dim_set, index)
coefficient = islhelper.isl_val_to_int(coefficient)
if coefficient != 0:
coefficients[symbol] = coefficient
@@ -156,55 +221,39 @@ 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))

-    @classmethod
-    def _fromsympy(cls, expr):
-        import sympy
-        equalities = []
-        inequalities = []
-        if expr.func == sympy.And:
-            for arg in expr.args:
-                arg_eqs, arg_ins = cls._fromsympy(arg)
-                equalities.extend(arg_eqs)
-                inequalities.extend(arg_ins)
-        elif expr.func == sympy.Eq:
-            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            equalities.append(expr)
-        else:
-            if expr.func == sympy.Lt:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
-            elif expr.func == sympy.Le:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
-            elif expr.func == sympy.Ge:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            elif expr.func == sympy.Gt:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
-            else:
-                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
-            inequalities.append(expr)
-        return equalities, inequalities
+
+    def _repr_latex_(self):
+        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):
-        import sympy
-        equalities, inequalities = cls._fromsympy(expr)
-        return cls(equalities, inequalities)
+    """
+    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:
@@ -213,48 +262,112 @@ 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):
-        if isinstance(left, numbers.Rational):
-            left = Constant(left)
-        elif not isinstance(left, Expression):
-            raise TypeError('left must be a a rational number '
-                'or a linear expression')
-        if isinstance(right, numbers.Rational):
-            right = Constant(right)
-        elif not isinstance(right, Expression):
-            raise TypeError('right must be a a rational number '
-                'or a linear expression')
+        if not isinstance(left, Expression):
+            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 isinstance(right, numbers.Rational):
+                right = Rational(right)
+            else:
+                raise TypeError('right must be a a rational number '
+                    'or a linear expression')
return func(left, right)
return wrapper

@_polymorphic
def Lt(left, right):
+    """
+    Assert first set is less than the second set.
+    """
return Polyhedron([], [right - left - 1])

@_polymorphic
def Le(left, right):
+    """
+    Assert first set is less than or equal to the second set.
+    """
return Polyhedron([], [right - left])

@_polymorphic
def Eq(left, right):
+    """
+    Assert first set is equal to the second set.
+    """
return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
+    """
+    Assert first set is not equal to the second set.
+    """
return ~Eq(left, right)

@_polymorphic
def Gt(left, right):
+    """
+    Assert first set is greater than the second set.
+    """
return Polyhedron([], [left - right - 1])

@_polymorphic
def Ge(left, right):
+    """
+    Assert first set is greater than or equal to the second set.
+    """
return Polyhedron([], [left - right])

-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])