X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/d1592edb29b12dafe5c0d0698310b98b4915cf26..HEAD:/linpy/domains.py?ds=inline

diff --git a/linpy/domains.py b/linpy/domains.py
index da0ea97..a431a02 100644
--- a/linpy/domains.py
+++ b/linpy/domains.py
@@ -23,14 +23,16 @@ import math
 from fractions import Fraction
 
 from . import islhelper
-from .islhelper import mainctx, libisl
-from .linexprs import LinExpr, Symbol, Rational
 from .geometry import GeometricObject, Point, Vector
+from .islhelper import libisl
+from .linexprs import LinExpr, Symbol
 
 
 __all__ = [
+    'And',
     'Domain',
-    'And', 'Or', 'Not',
+    'Not',
+    'Or',
 ]
 
 
@@ -38,7 +40,7 @@ __all__ = [
 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.
@@ -54,22 +56,23 @@ class Domain(GeometricObject):
         """
         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
-        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:
 
-        >>> 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.
@@ -83,7 +86,7 @@ class Domain(GeometricObject):
                 return argument.aspolyhedron()
             else:
                 raise TypeError('argument must be a string '
-                    'or a GeometricObject instance')
+                                'or a GeometricObject instance')
         else:
             for polyhedron in polyhedra:
                 if not isinstance(polyhedron, Polyhedron):
@@ -234,7 +237,7 @@ class Domain(GeometricObject):
         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):
@@ -288,11 +291,12 @@ class Domain(GeometricObject):
             if symbol in symbols:
                 n += 1
             elif n > 0:
-                islset = libisl.isl_set_project_out(islset,
-                    libisl.isl_dim_set, index + 1, n)
+                islset = libisl.isl_set_project_out(
+                    islset, libisl.isl_dim_set, index + 1, n)
                 n = 0
         if n > 0:
-            islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
+            islset = libisl.isl_set_project_out(
+                islset, libisl.isl_dim_set, 0, n)
         symbols = [symbol for symbol in self.symbols if symbol not in symbols]
         return Domain._fromislset(islset, symbols)
 
@@ -308,8 +312,8 @@ class Domain(GeometricObject):
             raise ValueError('domain must be non-empty')
         point = {}
         for index, symbol in enumerate(self.symbols):
-            coordinate = libisl.isl_point_get_coordinate_val(islpoint,
-                libisl.isl_dim_set, index)
+            coordinate = libisl.isl_point_get_coordinate_val(
+                islpoint, libisl.isl_dim_set, index)
             coordinate = islhelper.isl_val_to_int(coordinate)
             point[symbol] = coordinate
         libisl.isl_point_free(islpoint)
@@ -340,35 +344,39 @@ class Domain(GeometricObject):
         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:
-            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):
-        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):
-        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.
         """
-        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):
-        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):
@@ -387,43 +395,48 @@ class Domain(GeometricObject):
         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):
         """
         Return the vertices of the domain, as a list of rational instances of
         Point.
         """
-        from .polyhedra import Polyhedron
         if not self.isbounded():
             raise ValueError('domain must be bounded')
         islbset = self._toislbasicset(self.equalities, self.inequalities,
-            self.symbols)
-        vertices = libisl.isl_basic_set_compute_vertices(islbset);
+                                      self.symbols)
+        vertices = libisl.isl_basic_set_compute_vertices(islbset)
         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 = []
-            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 = libisl.isl_constraint_get_constant_val(
+                        constraint)
                     constant = islhelper.isl_val_to_int(constant)
                     for index, symbol in enumerate(self.symbols):
-                        coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
-                            libisl.isl_dim_set, index)
+                        coefficient = \
+                            libisl.isl_constraint_get_coefficient_val(
+                                constraint, libisl.isl_dim_set, index)
                         coefficient = islhelper.isl_val_to_int(coefficient)
                         if coefficient != 0:
                             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'))
                     denominator = match.group('den')
-                    denominator = 1 if denominator is None else int(denominator)
+                    denominator = \
+                        1 if denominator is None else int(denominator)
                     coordinate = Fraction(numerator, denominator)
                     coordinates.append((symbol, coordinate))
             points.append(Point(coordinates))
@@ -432,20 +445,19 @@ class Domain(GeometricObject):
     def points(self):
         """
         Return the integer points of a bounded domain, as a list of integer
-        instances of Point. If the domain is not bounded, a ValueError exception
-        is raised.
+        instances of Point. If the domain is not bounded, a ValueError
+        exception is raised.
         """
         if not self.isbounded():
             raise ValueError('domain must be bounded')
-        from .polyhedra import Universe, Eq
         islset = self._toislset(self.polyhedra, self.symbols)
         islpoints = islhelper.isl_set_points(islset)
         points = []
         for islpoint in islpoints:
             coordinates = {}
             for index, symbol in enumerate(self.symbols):
-                coordinate = libisl.isl_point_get_coordinate_val(islpoint,
-                    libisl.isl_dim_set, index)
+                coordinate = libisl.isl_point_get_coordinate_val(
+                    islpoint, libisl.isl_dim_set, index)
                 coordinate = islhelper.isl_val_to_int(coordinate)
                 coordinates[symbol] = coordinate
             points.append(Point(coordinates))
@@ -592,7 +604,7 @@ class Domain(GeometricObject):
         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 two or three-dimensional')
 
     def subs(self, symbol, expression=None):
         """
@@ -602,7 +614,7 @@ class Domain(GeometricObject):
         similar to LinExpr.subs().
         """
         polyhedra = [polyhedron.subs(symbol, expression)
-            for polyhedron in self.polyhedra]
+                     for polyhedron in self.polyhedra]
         return Domain(*polyhedra)
 
     @classmethod
@@ -630,12 +642,12 @@ class Domain(GeometricObject):
     @classmethod
     def _toislset(cls, polyhedra, symbols):
         polyhedron = polyhedra[0]
-        islbset = polyhedron._toislbasicset(polyhedron.equalities,
-            polyhedron.inequalities, symbols)
+        islbset = polyhedron._toislbasicset(
+            polyhedron.equalities, polyhedron.inequalities, symbols)
         islset1 = libisl.isl_set_from_basic_set(islbset)
         for polyhedron in polyhedra[1:]:
-            islbset = polyhedron._toislbasicset(polyhedron.equalities,
-                polyhedron.inequalities, symbols)
+            islbset = polyhedron._toislbasicset(
+                polyhedron.equalities, polyhedron.inequalities, symbols)
             islset2 = libisl.isl_set_from_basic_set(islbset)
             islset1 = libisl.isl_set_union(islset1, islset2)
         return islset1
@@ -696,17 +708,17 @@ class Domain(GeometricObject):
         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)
-        # replace '=' by '=='
+        # Replace '=' by '=='.
         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)
-        # 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)
-        # 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:
@@ -721,16 +733,10 @@ class Domain(GeometricObject):
         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
-    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
@@ -740,19 +746,19 @@ class Domain(GeometricObject):
             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):
         """
-        Convert the domain to a sympy expression.
+        Convert the domain to a SymPy expression.
         """
         import sympy
-        polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
+        polyhedra = [polyhedron.tosympy() for polyhedron in self.polyhedra]
         return sympy.Or(*polyhedra)
 
 
@@ -765,7 +771,7 @@ def And(*domains):
         return Universe
     else:
         return domains[0].intersection(*domains[1:])
-And.__doc__ = Domain.intersection.__doc__
+
 
 def Or(*domains):
     """
@@ -776,11 +782,10 @@ def Or(*domains):
         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
-Not.__doc__ = Domain.complement.__doc__