Fix error message

[linpy.git] / linpy / domains.py

diff --git a/linpy/domains.py b/linpy/domains.py
index 0da0a49..a431a02 100644 (file)
--- a/linpy/domains.py
+++ b/linpy/domains.py
@@ -23,14 +23,16 @@ import math
 from fractions import Fraction
 
 from . import islhelper
 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 .geometry import GeometricObject, Point, Vector

+from .islhelper import libisl
+from .linexprs import LinExpr, Symbol

 
 
 __all__ = [
 
 
 __all__ = [

+    'And',

     'Domain',
     '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
 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 +56,23 @@ 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.


@@ -83,7 +86,7 @@ class Domain(GeometricObject):
                 return argument.aspolyhedron()
             else:
                 raise TypeError('argument must be a string '
                 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):
         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)
         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):


@@ -288,11 +291,12 @@ class Domain(GeometricObject):
             if symbol in symbols:
                 n += 1
             elif n > 0:
             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:
                 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)
 
         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):
             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)
             coordinate = islhelper.isl_val_to_int(coordinate)
             point[symbol] = coordinate
         libisl.isl_point_free(islpoint)


@@ -401,36 +405,38 @@ class Domain(GeometricObject):
         Return the vertices of the domain, as a list of rational instances of
         Point.
         """
         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,
         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:
         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 self._RE_COORDINATE is None:
             coordinates = []
             if self._RE_COORDINATE is None:

-                constraints = islhelper.isl_basic_set_constraints(expr)
+                constraints = islhelper.isl_basic_set_constraints(expression)

                 for constraint in constraints:
                 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):
                     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:
                         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')
                 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))
                     coordinate = Fraction(numerator, denominator)
                     coordinates.append((symbol, coordinate))
             points.append(Point(coordinates))


@@ -439,20 +445,19 @@ class Domain(GeometricObject):
     def points(self):
         """
         Return the integer points of a bounded domain, as a list of integer
     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')
         """
         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):
         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))
                 coordinate = islhelper.isl_val_to_int(coordinate)
                 coordinates[symbol] = coordinate
             points.append(Point(coordinates))


@@ -599,7 +604,7 @@ 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('domain must be 2 or 3-dimensional')
+            raise ValueError('domain must be two or three-dimensional')

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


@@ -609,7 +614,7 @@ class Domain(GeometricObject):
         similar to LinExpr.subs().
         """
         polyhedra = [polyhedron.subs(symbol, expression)
         similar to LinExpr.subs().
         """
         polyhedra = [polyhedron.subs(symbol, expression)

-            for polyhedron in self.polyhedra]
+                     for polyhedron in self.polyhedra]

         return Domain(*polyhedra)
 
     @classmethod
         return Domain(*polyhedra)
 
     @classmethod


@@ -637,12 +642,12 @@ class Domain(GeometricObject):
     @classmethod
     def _toislset(cls, polyhedra, symbols):
         polyhedron = polyhedra[0]
     @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:]:
         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
             islset2 = libisl.isl_set_from_basic_set(islbset)
             islset1 = libisl.isl_set_union(islset1, islset2)
         return islset1


@@ -703,17 +708,17 @@ 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:


@@ -728,14 +733,8 @@ 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.
         """


@@ -747,19 +746,19 @@ 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):
         """
         Convert the domain to a SymPy expression.
         """
         import sympy
 
     def tosympy(self):
         """
         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)
 
 
         return sympy.Or(*polyhedra)
 
 


@@ -772,7 +771,7 @@ 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):
     """


@@ -783,11 +782,10 @@ 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__