Version 1.0.1

[linpy.git] / linpy / domains.py

diff --git a/linpy/domains.py b/linpy/domains.py
index 4cd46a4..f26b2fc 100644 (file)
--- a/linpy/domains.py
+++ b/linpy/domains.py
@@ -24,7 +24,7 @@ from fractions import Fraction
 
 from . import islhelper
 from .islhelper import mainctx, libisl
 
 from . import islhelper
 from .islhelper import mainctx, libisl

-from .linexprs import LinExpr, Symbol, Rational
+from .linexprs import LinExpr, Symbol

 from .geometry import GeometricObject, Point, Vector
 
 
 from .geometry import GeometricObject, Point, Vector
 
 


@@ -38,7 +38,7 @@ __all__ = [
 class Domain(GeometricObject):
     """
     A domain is a union of polyhedra. Unlike polyhedra, domains allow exact
 class Domain(GeometricObject):
     """
     A domain is a union of polyhedra. Unlike polyhedra, domains allow exact

-    computation of union and complementary operations.
+    computation of union, subtraction and complementary operations.

 
     A domain with a unique polyhedron is automatically subclassed as a
     Polyhedron instance.
 
     A domain with a unique polyhedron is automatically subclassed as a
     Polyhedron instance.


@@ -54,22 +54,23 @@ class Domain(GeometricObject):
         """
         Return a domain from a sequence of polyhedra.
 
         """
         Return a domain from a sequence of polyhedra.
 

-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
-        >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
-        >>> dom = Domain([square, square2])
+        >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+        >>> dom = Domain(square1, square2)
+        >>> dom
+        Or(And(x <= 2, 0 <= x, y <= 2, 0 <= y),
+           And(x <= 3, 1 <= x, y <= 3, 1 <= y))

 
         It is also possible to build domains from polyhedra using arithmetic
 
         It is also possible to build domains from polyhedra using arithmetic

-        operators Domain.__and__(), Domain.__or__() or functions And() and Or(),
-        using one of the following instructions:
+        operators Domain.__or__(), Domain.__invert__() or functions Or() and
+        Not(), using one of the following instructions:

 
 

-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
-        >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
-        >>> dom = square | square2
-        >>> dom = Or(square, square2)
+        >>> dom = square1 | square2
+        >>> dom = Or(square1, square2)

 
         Alternatively, a domain can be built from a string:
 
 
         Alternatively, a domain can be built from a string:
 

-        >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 2 <= x <= 4, 2 <= y <= 4')
+        >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 1 <= x <= 3, 1 <= y <= 3')

 
         Finally, a domain can be built from a GeometricObject instance, calling
         the GeometricObject.asdomain() method.
 
         Finally, a domain can be built from a GeometricObject instance, calling
         the GeometricObject.asdomain() method.


@@ -161,18 +162,22 @@ class Domain(GeometricObject):
         """
         Return True if two domains are equal.
         """
         """
         Return True if two domains are equal.
         """

-        symbols = self._xsymbols([self, other])
-        islset1 = self._toislset(self.polyhedra, symbols)
-        islset2 = other._toislset(other.polyhedra, symbols)
-        equal = bool(libisl.isl_set_is_equal(islset1, islset2))
-        libisl.isl_set_free(islset1)
-        libisl.isl_set_free(islset2)
-        return equal
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = other._toislset(other.polyhedra, symbols)
+            equal = bool(libisl.isl_set_is_equal(islset1, islset2))
+            libisl.isl_set_free(islset1)
+            libisl.isl_set_free(islset2)
+            return equal
+        return NotImplemented

 
     def isdisjoint(self, other):
         """
         Return True if two domains have a null intersection.
         """
 
     def isdisjoint(self, other):
         """
         Return True if two domains have a null intersection.
         """

+        if not isinstance(other, Domain):
+            raise TypeError('other must be a Domain instance')

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -185,29 +190,33 @@ class Domain(GeometricObject):
         """
         Report whether another domain contains the domain.
         """
         """
         Report whether another domain contains the domain.
         """

-        symbols = self._xsymbols([self, other])
-        islset1 = self._toislset(self.polyhedra, symbols)
-        islset2 = self._toislset(other.polyhedra, symbols)
-        equal = bool(libisl.isl_set_is_subset(islset1, islset2))
-        libisl.isl_set_free(islset1)
-        libisl.isl_set_free(islset2)
-        return equal
+        return self < other

 
     def __le__(self, other):
 
     def __le__(self, other):

-        return self.issubset(other)
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = self._toislset(other.polyhedra, symbols)
+            equal = bool(libisl.isl_set_is_subset(islset1, islset2))
+            libisl.isl_set_free(islset1)
+            libisl.isl_set_free(islset2)
+            return equal
+        return NotImplemented

     __le__.__doc__ = issubset.__doc__
 
     def __lt__(self, other):
         """
         Report whether another domain is contained within the domain.
         """
     __le__.__doc__ = issubset.__doc__
 
     def __lt__(self, other):
         """
         Report whether another domain is contained within the domain.
         """

-        symbols = self._xsymbols([self, other])
-        islset1 = self._toislset(self.polyhedra, symbols)
-        islset2 = self._toislset(other.polyhedra, symbols)
-        equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
-        libisl.isl_set_free(islset1)
-        libisl.isl_set_free(islset2)
-        return equal
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = self._toislset(other.polyhedra, symbols)
+            equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
+            libisl.isl_set_free(islset1)
+            libisl.isl_set_free(islset2)
+            return equal
+        return NotImplemented

 
     def complement(self):
         """
 
     def complement(self):
         """


@@ -226,7 +235,7 @@ class Domain(GeometricObject):
         Return an equivalent domain, whose polyhedra are disjoint.
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         Return an equivalent domain, whose polyhedra are disjoint.
         """
         islset = self._toislset(self.polyhedra, self.symbols)

-        islset = libisl.isl_set_make_disjoint(mainctx, islset)
+        islset = libisl.isl_set_make_disjoint(islset)

         return self._fromislset(islset, self.symbols)
 
     def coalesce(self):
         return self._fromislset(islset, self.symbols)
 
     def coalesce(self):


@@ -270,6 +279,10 @@ class Domain(GeometricObject):
         Project out the sequence of symbols given in arguments, and return the
         resulting domain.
         """
         Project out the sequence of symbols given in arguments, and return the
         resulting domain.
         """

+        symbols = list(symbols)
+        for symbol in symbols:
+            if not isinstance(symbol, Symbol):
+                raise TypeError('symbols must be Symbol instances')

         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):
         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):


@@ -308,17 +321,19 @@ class Domain(GeometricObject):
         Return the intersection of two or more domains as a new domain. As an
         alternative, function And() can be used.
         """
         Return the intersection of two or more domains as a new domain. As an
         alternative, function And() can be used.
         """

-        if len(others) == 0:
-            return self
-        symbols = self._xsymbols((self,) + others)
-        islset1 = self._toislset(self.polyhedra, symbols)
+        result = self

         for other in others:
         for other in others:

-            islset2 = other._toislset(other.polyhedra, symbols)
-            islset1 = libisl.isl_set_intersect(islset1, islset2)
-        return self._fromislset(islset1, symbols)
+            result &= other
+        return result

 
     def __and__(self, other):
 
     def __and__(self, other):

-        return self.intersection(other)
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = other._toislset(other.polyhedra, symbols)
+            islset = libisl.isl_set_intersect(islset1, islset2)
+            return self._fromislset(islset, symbols)
+        return NotImplemented

     __and__.__doc__ = intersection.__doc__
 
     def union(self, *others):
     __and__.__doc__ = intersection.__doc__
 
     def union(self, *others):


@@ -326,35 +341,39 @@ class Domain(GeometricObject):
         Return the union of two or more domains as a new domain. As an
         alternative, function Or() can be used.
         """
         Return the union of two or more domains as a new domain. As an
         alternative, function Or() can be used.
         """

-        if len(others) == 0:
-            return self
-        symbols = self._xsymbols((self,) + others)
-        islset1 = self._toislset(self.polyhedra, symbols)
+        result = self

         for other in others:
         for other in others:

-            islset2 = other._toislset(other.polyhedra, symbols)
-            islset1 = libisl.isl_set_union(islset1, islset2)
-        return self._fromislset(islset1, symbols)
+            result |= other
+        return result

 
     def __or__(self, other):
 
     def __or__(self, other):

-        return self.union(other)
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = other._toislset(other.polyhedra, symbols)
+            islset = libisl.isl_set_union(islset1, islset2)
+            return self._fromislset(islset, symbols)
+        return NotImplemented

     __or__.__doc__ = union.__doc__
 
     def __add__(self, other):
     __or__.__doc__ = union.__doc__
 
     def __add__(self, other):

-        return self.union(other)
+        return self | other

     __add__.__doc__ = union.__doc__
 
     def difference(self, other):
         """
         Return the difference of two domains as a new domain.
         """
     __add__.__doc__ = union.__doc__
 
     def difference(self, other):
         """
         Return the difference of two domains as a new domain.
         """

-        symbols = self._xsymbols([self, other])
-        islset1 = self._toislset(self.polyhedra, symbols)
-        islset2 = other._toislset(other.polyhedra, symbols)
-        islset = libisl.isl_set_subtract(islset1, islset2)
-        return self._fromislset(islset, symbols)
+        return self - other

 
     def __sub__(self, other):
 
     def __sub__(self, other):

-        return self.difference(other)
+        if isinstance(other, Domain):
+            symbols = self._xsymbols([self, other])
+            islset1 = self._toislset(self.polyhedra, symbols)
+            islset2 = other._toislset(other.polyhedra, symbols)
+            islset = libisl.isl_set_subtract(islset1, islset2)
+            return self._fromislset(islset, symbols)
+        return NotImplemented

     __sub__.__doc__ = difference.__doc__
 
     def lexmin(self):
     __sub__.__doc__ = difference.__doc__
 
     def lexmin(self):


@@ -373,7 +392,10 @@ class Domain(GeometricObject):
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 

-    _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+    if islhelper.isl_version >= '0.13':
+        _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+    else:
+        _RE_COORDINATE = None

 
     def vertices(self):
         """
 
     def vertices(self):
         """


@@ -389,10 +411,10 @@ class Domain(GeometricObject):
         vertices = islhelper.isl_vertices_vertices(vertices)
         points = []
         for vertex in vertices:
         vertices = islhelper.isl_vertices_vertices(vertices)
         points = []
         for vertex in vertices:

-            expr = libisl.isl_vertex_get_expr(vertex)
+            expression = libisl.isl_vertex_get_expr(vertex)

             coordinates = []
             coordinates = []

-            if islhelper.isl_version < '0.13':
-                constraints = islhelper.isl_basic_set_constraints(expr)
+            if self._RE_COORDINATE is None:
+                constraints = islhelper.isl_basic_set_constraints(expression)

                 for constraint in constraints:
                     constant = libisl.isl_constraint_get_constant_val(constraint)
                     constant = islhelper.isl_val_to_int(constant)
                 for constraint in constraints:
                     constant = libisl.isl_constraint_get_constant_val(constraint)
                     constant = islhelper.isl_val_to_int(constant)


@@ -404,7 +426,7 @@ class Domain(GeometricObject):
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:

-                string = islhelper.isl_multi_aff_to_str(expr)
+                string = islhelper.isl_multi_aff_to_str(expression)

                 matches = self._RE_COORDINATE.finditer(string)
                 for symbol, match in zip(self.symbols, matches):
                     numerator = int(match.group('num'))
                 matches = self._RE_COORDINATE.finditer(string)
                 for symbol, match in zip(self.symbols, matches):
                     numerator = int(match.group('num'))


@@ -578,7 +600,7 @@ class Domain(GeometricObject):
         elif self.dimension == 3:
             return self._plot_3d(plot=plot, **kwargs)
         else:
         elif self.dimension == 3:
             return self._plot_3d(plot=plot, **kwargs)
         else:

-            raise ValueError('polyhedron must be 2 or 3-dimensional')
+            raise ValueError('domain must be 2 or 3-dimensional')

 
     def subs(self, symbol, expression=None):
         """
 
     def subs(self, symbol, expression=None):
         """


@@ -682,17 +704,17 @@ class Domain(GeometricObject):
         Create a domain from a string. Raise SyntaxError if the string is not
         properly formatted.
         """
         Create a domain from a string. Raise SyntaxError if the string is not
         properly formatted.
         """

-        # remove curly brackets
+        # Remove curly brackets.

         string = cls._RE_BRACES.sub(r'', string)
         string = cls._RE_BRACES.sub(r'', string)

-        # replace '=' by '=='
+        # Replace '=' by '=='.

         string = cls._RE_EQ.sub(r'\1==\2', string)
         string = cls._RE_EQ.sub(r'\1==\2', string)

-        # replace 'and', 'or', 'not'
+        # Replace 'and', 'or', 'not'.

         string = cls._RE_AND.sub(r' & ', string)
         string = cls._RE_OR.sub(r' | ', string)
         string = cls._RE_NOT.sub(r' ~', string)
         string = cls._RE_AND.sub(r' & ', string)
         string = cls._RE_OR.sub(r' | ', string)
         string = cls._RE_NOT.sub(r' ~', string)

-        # add implicit multiplication operators, e.g. '5x' -> '5*x'
+        # Add implicit multiplication operators, e.g. '5x' -> '5*x'.

         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)

-        # add parentheses to force precedence
+        # Add parentheses to force precedence.

         tokens = cls._RE_OPERATORS.split(string)
         for i, token in enumerate(tokens):
             if i % 2 == 0:
         tokens = cls._RE_OPERATORS.split(string)
         for i, token in enumerate(tokens):
             if i % 2 == 0:


@@ -707,16 +729,10 @@ class Domain(GeometricObject):
         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
         return 'Or({})'.format(', '.join(strings))
 
         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
         return 'Or({})'.format(', '.join(strings))
 

-    def _repr_latex_(self):
-        strings = []
-        for polyhedron in self.polyhedra:
-            strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
-        return '${}$'.format(' \\vee '.join(strings))
-

     @classmethod
     @classmethod

-    def fromsympy(cls, expr):
+    def fromsympy(cls, expression):

         """
         """

-        Create a domain from a sympy expression.
+        Create a domain from a SymPy expression.

         """
         import sympy
         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
         """
         import sympy
         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt


@@ -726,16 +742,16 @@ class Domain(GeometricObject):
             sympy.Eq: Eq, sympy.Ne: Ne,
             sympy.Ge: Ge, sympy.Gt: Gt,
         }
             sympy.Eq: Eq, sympy.Ne: Ne,
             sympy.Ge: Ge, sympy.Gt: Gt,
         }

-        if expr.func in funcmap:
-            args = [Domain.fromsympy(arg) for arg in expr.args]
-            return funcmap[expr.func](*args)
-        elif isinstance(expr, sympy.Expr):
-            return LinExpr.fromsympy(expr)
-        raise ValueError('non-domain expression: {!r}'.format(expr))
+        if expression.func in funcmap:
+            args = [Domain.fromsympy(arg) for arg in expression.args]
+            return funcmap[expression.func](*args)
+        elif isinstance(expression, sympy.Expr):
+            return LinExpr.fromsympy(expression)
+        raise ValueError('non-domain expression: {!r}'.format(expression))

 
     def tosympy(self):
         """
 
     def tosympy(self):
         """

-        Convert the domain to a sympy expression.
+        Convert the domain to a SymPy expression.

         """
         import sympy
         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
         """
         import sympy
         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]


@@ -751,7 +767,6 @@ def And(*domains):
         return Universe
     else:
         return domains[0].intersection(*domains[1:])
         return Universe
     else:
         return domains[0].intersection(*domains[1:])

-And.__doc__ = Domain.intersection.__doc__

 
 def Or(*domains):
     """
 
 def Or(*domains):
     """


@@ -762,11 +777,9 @@ def Or(*domains):
         return Empty
     else:
         return domains[0].union(*domains[1:])
         return Empty
     else:
         return domains[0].union(*domains[1:])

-Or.__doc__ = Domain.union.__doc__

 
 def Not(domain):
     """
     Create the complementary domain of the domain given in argument.
     """
     return ~domain
 
 def Not(domain):
     """
     Create the complementary domain of the domain given in argument.
     """
     return ~domain

-Not.__doc__ = Domain.complement.__doc__