index 238248b..432e275 100644 (file)
# You should have received a copy of the GNU General Public License
# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.

-"""
-Polyhedral domains
-
-This module provides classes and functions to deal with polyhedral
-domains, i.e. unions of polyhedra.
-"""
-
import ast
import functools
import re
@@ -31,7 +24,7 @@ from fractions import Fraction

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

@@ -44,7 +37,11 @@ __all__ = [
@functools.total_ordering
class Domain(GeometricObject):
"""
-    This class represents polyhedral domains, i.e. unions of polyhedra.
+    A domain is a union of polyhedra. Unlike polyhedra, domains allow exact
+    computation of union, subtraction and complementary operations.
+
+    A domain with a unique polyhedron is automatically subclassed as a
+    Polyhedron instance.
"""

__slots__ = (
@@ -55,7 +52,28 @@ class Domain(GeometricObject):

def __new__(cls, *polyhedra):
"""
-        Create and return a new domain from a string or a list of polyhedra.
+        Return a domain from a sequence of polyhedra.
+
+        >>> 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.__or__(), Domain.__invert__() or functions Or() and
+        Not(), using one of the following instructions:
+
+        >>> dom = square1 | square2
+        >>> dom = Or(square1, square2)
+
+        Alternatively, a domain can be built from a string:
+
+        >>> 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.
"""
from .polyhedra import Polyhedron
if len(polyhedra) == 1:
@@ -88,35 +106,28 @@ class Domain(GeometricObject):
@property
def polyhedra(self):
"""
-        The tuple of polyhedra which constitute the domain.
+        The tuple of polyhedra present in the domain.
"""
return self._polyhedra

@property
def symbols(self):
"""
-        The tuple of symbols present in the domain equations.
+        The tuple of symbols present in the domain equations, sorted according
+        to Symbol.sortkey().
"""
return self._symbols

@property
def dimension(self):
"""
-        The dimension of the domain, i.e. the number of symbols.
+        The dimension of the domain, i.e. the number of symbols present in it.
"""
return self._dimension

-    def make_disjoint(self):
-        """
-        Return an equivalent domain, whose polyhedra are disjoint.
-        """
-        islset = self._toislset(self.polyhedra, self.symbols)
-        islset = libisl.isl_set_make_disjoint(mainctx, islset)
-        return self._fromislset(islset, self.symbols)
-
def isempty(self):
"""
-        Return True if the domain is empty.
+        Return True if the domain is empty, that is, equal to Empty.
"""
islset = self._toislset(self.polyhedra, self.symbols)
empty = bool(libisl.isl_set_is_empty(islset))
@@ -131,7 +142,7 @@ class Domain(GeometricObject):

def isuniverse(self):
"""
-        Return True if the domain is universal, i.e. with no constraint.
+        Return True if the domain is universal, that is, equal to Universe.
"""
islset = self._toislset(self.polyhedra, self.symbols)
universe = bool(libisl.isl_set_plain_is_universe(islset))
@@ -149,20 +160,24 @@ class Domain(GeometricObject):

def __eq__(self, other):
"""
-        Return True if the 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.
"""
+        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)
@@ -175,29 +190,33 @@ class Domain(GeometricObject):
"""
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):
-        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.
"""
-        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):
"""
@@ -211,10 +230,18 @@ class Domain(GeometricObject):
return self.complement()
__invert__.__doc__ = complement.__doc__

+    def make_disjoint(self):
+        """
+        Return an equivalent domain, whose polyhedra are disjoint.
+        """
+        islset = self._toislset(self.polyhedra, self.symbols)
+        islset = libisl.isl_set_make_disjoint(mainctx, islset)
+        return self._fromislset(islset, self.symbols)
+
def coalesce(self):
"""
Simplify the representation of the domain by trying to combine pairs of
-        polyhedra into a single polyhedron.
+        polyhedra into a single polyhedron, and return the resulting domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_coalesce(islset)
@@ -223,7 +250,7 @@ class Domain(GeometricObject):
def detect_equalities(self):
"""
Simplify the representation of the domain by detecting implicit
-        equalities.
+        equalities, and return the resulting domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_detect_equalities(islset)
@@ -231,16 +258,14 @@ class Domain(GeometricObject):

def remove_redundancies(self):
"""
-        Remove redundant constraints in the domain.
+        Remove redundant constraints in the domain, and return the resulting
+        domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_remove_redundancies(islset)
return self._fromislset(islset, self.symbols)

def aspolyhedron(self):
-        """
-        Return the polyhedral hull of the domain.
-        """
from .polyhedra import Polyhedron
islset = self._toislset(self.polyhedra, self.symbols)
islbset = libisl.isl_set_polyhedral_hull(islset)
@@ -251,8 +276,13 @@ class Domain(GeometricObject):

def project(self, symbols):
"""
-        Project out the symbols given in arguments.
+        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))):
@@ -269,7 +299,8 @@ class Domain(GeometricObject):

def sample(self):
"""
-        Return a sample of the domain.
+        Return a sample of the domain, as an integer instance of Point. If the
+        domain is empty, a ValueError exception is raised.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islpoint = libisl.isl_set_sample_point(islset)
@@ -287,54 +318,62 @@ class Domain(GeometricObject):

def intersection(self, *others):
"""
-        Return the intersection of two domains as a new domain.
+        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:
-            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):
-        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):
"""
-        Return the union of two domains as a new domain.
+        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__

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

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):
@@ -353,11 +392,15 @@ 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.
+        Return the vertices of the domain, as a list of rational instances of
+        Point.
"""
from .polyhedra import Polyhedron
if not self.isbounded():
@@ -370,7 +413,7 @@ class Domain(GeometricObject):
for vertex in vertices:
expr = libisl.isl_vertex_get_expr(vertex)
coordinates = []
-            if islhelper.isl_version < '0.13':
+            if self._RE_COORDINATE is None:
constraints = islhelper.isl_basic_set_constraints(expr)
for constraint in constraints:
constant = libisl.isl_constraint_get_constant_val(constraint)
@@ -396,7 +439,9 @@ class Domain(GeometricObject):

def points(self):
"""
-        Return the points with integer coordinates contained in the domain.
+        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.
"""
if not self.isbounded():
raise ValueError('domain must be bounded')
@@ -414,6 +459,15 @@ class Domain(GeometricObject):
points.append(Point(coordinates))
return points

+    def __contains__(self, point):
+        """
+        Return True if the point if contained within the domain.
+        """
+        for polyhedron in self.polyhedra:
+            if point in polyhedron:
+                return True
+        return False
+
@classmethod
def _polygon_inner_point(cls, points):
symbols = points.symbols
@@ -467,7 +521,9 @@ class Domain(GeometricObject):

def faces(self):
"""
-        Return the vertices of the domain, grouped by face.
+        Return the list of faces of a bounded domain. Each face is represented
+        by a list of vertices, in the form of rational instances of Point. If
+        the domain is not bounded, a ValueError exception is raised.
"""
faces = []
for polyhedron in self.polyhedra:
@@ -531,7 +587,11 @@ class Domain(GeometricObject):

def plot(self, plot=None, **kwargs):
"""
-        Plot the domain using matplotlib.
+        Plot a 2D or 3D domain using matplotlib. Draw it to the current plot
+        object if present, otherwise create a new one. options are keyword
+        arguments passed to the matplotlib drawing functions, they can be used
+        to set the drawing color for example. Raise ValueError is the domain is
+        not 2D or 3D.
"""
if not self.isbounded():
raise ValueError('domain must be bounded')
@@ -540,21 +600,14 @@ class Domain(GeometricObject):
elif self.dimension == 3:
return self._plot_3d(plot=plot, **kwargs)
else:
-            raise ValueError('polyhedron must be 2 or 3-dimensional')
-
-    def __contains__(self, point):
-        """
-        Return True if point if contained within the domain.
-        """
-        for polyhedron in self.polyhedra:
-            if point in polyhedron:
-                return True
-        return False
+            raise ValueError('domain must be 2 or 3-dimensional')

def subs(self, symbol, expression=None):
"""
-        Subsitute symbol by expression in equations and return the resulting
-        domain.
+        Substitute the given symbol by an expression in the domain constraints.
+        To perform multiple substitutions at once, pass a sequence or a
+        dictionary of (old, new) pairs to subs. The syntax of this function is
+        similar to LinExpr.subs().
"""
polyhedra = [polyhedron.subs(symbol, expression)
for polyhedron in self.polyhedra]
@@ -648,19 +701,20 @@ class Domain(GeometricObject):
@classmethod
def fromstring(cls, string):
"""
-        Convert a string into a domain.
+        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:
@@ -671,23 +725,14 @@ class Domain(GeometricObject):
return cls._fromast(tree)

def __repr__(self):
-        """
-        Return repr(self).
-        """
assert len(self.polyhedra) >= 2
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):
"""
-        Convert a SymPy expression into a domain.
+        Create a domain from a SymPy expression.
"""
import sympy
from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
@@ -706,7 +751,7 @@ class Domain(GeometricObject):

def tosympy(self):
"""
-        Convert a domain into a SymPy expression.
+        Convert the domain to a SymPy expression.
"""
import sympy
polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
@@ -714,21 +759,27 @@ class Domain(GeometricObject):

def And(*domains):
+    """
+    Create the intersection domain of the domains given in arguments.
+    """
if len(domains) == 0:
from .polyhedra import Universe
return Universe
else:
return domains.intersection(*domains[1:])
-And.__doc__ = Domain.intersection.__doc__

def Or(*domains):
+    """
+    Create the union domain of the domains given in arguments.
+    """
if len(domains) == 0:
from .polyhedra import Empty
return Empty
else:
return domains.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__