index 787e965..ccb1a8c 100644 (file)
@@ -1,12 +1,12 @@
-import ast
import functools
import functools
+import math
import numbers
import numbers
-import re

from . import islhelper

from .islhelper import mainctx, libisl

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

from .domains import Domain

@@ -32,28 +32,24 @@ class Polyhedron(Domain):
if inequalities is not None:
raise TypeError('too many arguments')
return cls.fromstring(equalities)
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')
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')
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')
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)
symbols = cls._xsymbols(equalities + inequalities)
islbset = cls._toislbasicset(equalities, inequalities, symbols)
return cls._fromislbasicset(islbset, symbols)
@@ -75,30 +71,88 @@ class Polyhedron(Domain):
return self,

def disjoint(self):
return self,

def disjoint(self):
+        """
+        Return this set as disjoint.
+        """
return self

def isuniverse(self):
return self

def isuniverse(self):
+        """
+        Return true if this 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

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 this set.
+        """
return self

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):
+        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):
@classmethod
def _fromislbasicset(cls, islbset, symbols):
+        if libisl.isl_basic_set_is_empty(islbset):
+            return Empty
+        if libisl.isl_basic_set_is_universe(islbset):
+            return Universe
islconstraints = islhelper.isl_basic_set_constraints(islbset)
equalities = []
inequalities = []
for islconstraint in islconstraints:
islconstraints = islhelper.isl_basic_set_constraints(islbset)
equalities = []
inequalities = []
for islconstraint in islconstraints:
-            islpr = libisl.isl_printer_to_str(mainctx)
constant = libisl.isl_constraint_get_constant_val(islconstraint)
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
constant = libisl.isl_constraint_get_constant_val(islconstraint)
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
-            for dim, symbol in enumerate(symbols):
-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, dim)
+            for index, symbol in enumerate(symbols):
+                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
coefficient = islhelper.isl_val_to_int(coefficient)
if coefficient != 0:
coefficients[symbol] = coefficient
@@ -119,134 +173,70 @@ class Polyhedron(Domain):
@classmethod
def _toislbasicset(cls, equalities, inequalities, symbols):
dimension = len(symbols)
@classmethod
def _toislbasicset(cls, equalities, inequalities, symbols):
dimension = len(symbols)
+        indices = {symbol: index for index, symbol in enumerate(symbols)}
islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
islls = libisl.isl_local_space_from_space(islsp)
for equality in equalities:
isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
for symbol, coefficient in equality.coefficients():
islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
islls = libisl.isl_local_space_from_space(islsp)
for equality in equalities:
isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
for symbol, coefficient in equality.coefficients():
-                val = str(coefficient).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                sid = symbols.index(symbol)
+                islval = str(coefficient).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                index = indices[symbol]
isleq = libisl.isl_constraint_set_coefficient_val(isleq,
isleq = libisl.isl_constraint_set_coefficient_val(isleq,
-                    libisl.isl_dim_set, sid, val)
+                    libisl.isl_dim_set, index, islval)
if equality.constant != 0:
if equality.constant != 0:
-                val = str(equality.constant).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                isleq = libisl.isl_constraint_set_constant_val(isleq, val)
+                islval = str(equality.constant).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
for inequality in inequalities:
islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
for symbol, coefficient in inequality.coefficients():
islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
for inequality in inequalities:
islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
for symbol, coefficient in inequality.coefficients():
-                val = str(coefficient).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                sid = symbols.index(symbol)
+                islval = str(coefficient).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                index = indices[symbol]
islin = libisl.isl_constraint_set_coefficient_val(islin,
islin = libisl.isl_constraint_set_coefficient_val(islin,
-                    libisl.isl_dim_set, sid, val)
+                    libisl.isl_dim_set, index, islval)
if inequality.constant != 0:
if inequality.constant != 0:
-                val = str(inequality.constant).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                islin = libisl.isl_constraint_set_constant_val(islin, val)
+                islval = str(inequality.constant).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                islin = libisl.isl_constraint_set_constant_val(islin, islval)
islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
return islbset

islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
return islbset

-    @classmethod
-    def _fromast(cls, node):
-        if isinstance(node, ast.Module) and len(node.body) == 1:
-            return cls._fromast(node.body)
-        elif isinstance(node, ast.Expr):
-            return cls._fromast(node.value)
-        elif isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitAnd):
-            equalities1, inequalities1 = cls._fromast(node.left)
-            equalities2, inequalities2 = cls._fromast(node.right)
-            equalities = equalities1 + equalities2
-            inequalities = inequalities1 + inequalities2
-            return equalities, inequalities
-        elif isinstance(node, ast.Compare):
-            equalities = []
-            inequalities = []
-            left = Expression._fromast(node.left)
-            for i in range(len(node.ops)):
-                op = node.ops[i]
-                right = Expression._fromast(node.comparators[i])
-                if isinstance(op, ast.Lt):
-                    inequalities.append(right - left - 1)
-                elif isinstance(op, ast.LtE):
-                    inequalities.append(right - left)
-                elif isinstance(op, ast.Eq):
-                    equalities.append(left - right)
-                elif isinstance(op, ast.GtE):
-                    inequalities.append(left - right)
-                elif isinstance(op, ast.Gt):
-                    inequalities.append(left - right - 1)
-                else:
-                    break
-                left = right
-            else:
-                return equalities, inequalities
-        raise SyntaxError('invalid syntax')
-
@classmethod
def fromstring(cls, string):
@classmethod
def fromstring(cls, string):
-        string = string.strip()
-        string = re.sub(r'^\{\s*|\s*\}\$', '', string)
-        string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
-        string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
-        tokens = re.split(r',|;|and|&&|/\\|∧', string, flags=re.I)
-        tokens = ['({})'.format(token) for token in tokens]
-        string = ' & '.join(tokens)
-        tree = ast.parse(string, 'eval')
-        equalities, inequalities = cls._fromast(tree)
-        return cls(equalities, inequalities)
+        domain = Domain.fromstring(string)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(string))
+        return domain

def __repr__(self):

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
else:
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
-            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 - expr.args)
-            equalities.append(expr)
-        else:
-            if expr.func == sympy.Lt:
-                expr = Expression.fromsympy(expr.args - expr.args - 1)
-            elif expr.func == sympy.Le:
-                expr = Expression.fromsympy(expr.args - expr.args)
-            elif expr.func == sympy.Ge:
-                expr = Expression.fromsympy(expr.args - expr.args)
-            elif expr.func == sympy.Gt:
-                expr = Expression.fromsympy(expr.args - expr.args - 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):

@classmethod
def fromsympy(cls, expr):
-        import sympy
-        equalities, inequalities = cls._fromsympy(expr)
-        return cls(equalities, inequalities)
+        domain = Domain.fromsympy(expr)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+        return domain

def tosympy(self):
import sympy

def tosympy(self):
import sympy
@@ -258,47 +248,111 @@ class Polyhedron(Domain):
return sympy.And(*constraints)

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):
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):
return func(left, right)
return wrapper

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

@_polymorphic
def Le(left, right):
return Polyhedron([], [right - left - 1])

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

@_polymorphic
def Eq(left, right):
return Polyhedron([], [right - left])

@_polymorphic
def Eq(left, right):
+    """
+    Return true if the sets are equal.
+    """
return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
+    """
+    Return true if the sets are NOT equal.
+    """
return ~Eq(left, right)

@_polymorphic
def Gt(left, right):
return ~Eq(left, right)

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

@_polymorphic
def Ge(left, right):
return Polyhedron([], [left - right - 1])

@_polymorphic
def Ge(left, right):
+    """
+    Return true if the first set is greater than or equal the second set.
+    """
return Polyhedron([], [left - right])
return Polyhedron([], [left - right])
-
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])