index 1ccbe9c..9e740a4 100644 (file)
# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.

import functools
-import math
import numbers

from . import islhelper

-from .islhelper import mainctx, libisl
+from .domains import Domain
from .geometry import GeometricObject, Point
+from .islhelper import libisl, mainctx
from .linexprs import LinExpr, Rational
-from .domains import Domain

__all__ = [
+    'Empty',
+    'Eq',
+    'Ge',
+    'Gt',
+    'Le',
+    'Lt',
+    'Ne',
'Polyhedron',
-    'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
-    'Empty', 'Universe',
+    'Universe',
]

class Polyhedron(Domain):
"""
A convex polyhedron (or simply "polyhedron") is the space defined by a
-    system of linear equalities and inequalities. This space can be unbounded. A
-    Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
+    system of linear equalities and inequalities. This space can be unbounded.
+    Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
points in a convex polyhedron.
"""

@@ -51,9 +56,9 @@ class Polyhedron(Domain):

def __new__(cls, equalities=None, inequalities=None):
"""
-        Return a polyhedron from two sequences of linear expressions: equalities
-        is a list of expressions equal to 0, and inequalities is a list of
-        expressions greater or equal to 0. For example, the polyhedron
+        Return a polyhedron from two sequences of linear expressions:
+        equalities is a list of expressions equal to 0, and inequalities is a
+        list of expressions greater or equal to 0. For example, the polyhedron
0 <= x <= 2, 0 <= y <= 2 can be constructed with:

>>> x, y = symbols('x y')
@@ -62,8 +67,9 @@ class Polyhedron(Domain):
And(0 <= x, x <= 2, 0 <= y, y <= 2)

It may be easier to use comparison operators LinExpr.__lt__(),
-        LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(),
-        Le(), Eq(), Ge() and Gt(), using one of the following instructions:
+        LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or
+        functions Lt(), Le(), Eq(), Ge() and Gt(), using one of the following
+        instructions:

>>> x, y = symbols('x y')
>>> square1 = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
@@ -74,9 +80,9 @@ class Polyhedron(Domain):
>>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')

Finally, a polyhedron can be constructed from a GeometricObject
-        instance, calling the GeometricObject.aspolyedron() method. This way, it
-        is possible to compute the polyhedral hull of a Domain instance, i.e.,
-        the convex hull of two polyhedra:
+        instance, calling the GeometricObject.aspolyedron() method. This way,
+        it is possible to compute the polyhedral hull of a Domain instance,
+        i.e., the convex hull of two polyhedra:

>>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
>>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
@@ -94,15 +100,23 @@ class Polyhedron(Domain):
sc_equalities = []
if equalities is not None:
for equality in equalities:
-                if not isinstance(equality, LinExpr):
-                    raise TypeError('equalities must be linear expressions')
-                sc_equalities.append(equality.scaleint())
+                if isinstance(equality, LinExpr):
+                    sc_equalities.append(equality.scaleint())
+                elif isinstance(equality, numbers.Rational):
+                    sc_equalities.append(Rational(equality).scaleint())
+                else:
+                    raise TypeError('equalities must be linear expressions '
+                                    'or rational numbers')
sc_inequalities = []
if inequalities is not None:
for inequality in inequalities:
-                if not isinstance(inequality, LinExpr):
-                    raise TypeError('inequalities must be linear expressions')
-                sc_inequalities.append(inequality.scaleint())
+                if isinstance(inequality, LinExpr):
+                    sc_inequalities.append(inequality.scaleint())
+                elif isinstance(inequality, numbers.Rational):
+                    sc_inequalities.append(Rational(inequality).scaleint())
+                else:
+                    raise TypeError('inequalities must be linear expressions '
+                                    'or rational numbers')
symbols = cls._xsymbols(sc_equalities + sc_inequalities)
islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
return cls._fromislbasicset(islbset, symbols)
@@ -140,7 +154,7 @@ class Polyhedron(Domain):

def isuniverse(self):
islbset = self._toislbasicset(self.equalities, self.inequalities,
-            self.symbols)
+                                      self.symbols)
universe = bool(libisl.isl_basic_set_is_universe(islbset))
libisl.isl_basic_set_free(islbset)
return universe
@@ -172,9 +186,9 @@ class Polyhedron(Domain):

def subs(self, symbol, expression=None):
equalities = [equality.subs(symbol, expression)
-            for equality in self.equalities]
+                      for equality in self.equalities]
inequalities = [inequality.subs(symbol, expression)
-            for inequality in self.inequalities]
+                        for inequality in self.inequalities]
return Polyhedron(equalities, inequalities)

def asinequalities(self):
@@ -214,6 +228,10 @@ class Polyhedron(Domain):

@classmethod
def _fromislbasicset(cls, islbset, symbols):
+        if bool(libisl.isl_basic_set_is_empty(islbset)):
+            return Empty
+        if bool(libisl.isl_basic_set_is_universe(islbset)):
+            return Universe
islconstraints = islhelper.isl_basic_set_constraints(islbset)
equalities = []
inequalities = []
@@ -222,8 +240,8 @@ class Polyhedron(Domain):
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
for index, symbol in enumerate(symbols):
-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
-                    libisl.isl_dim_set, index)
+                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
@@ -248,26 +266,28 @@ class Polyhedron(Domain):
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))
+            isleq = libisl.isl_equality_alloc(
+                libisl.isl_local_space_copy(islls))
for symbol, coefficient in equality.coefficients():
islval = str(coefficient).encode()
index = indices[symbol]
-                isleq = libisl.isl_constraint_set_coefficient_val(isleq,
-                    libisl.isl_dim_set, index, islval)
+                isleq = libisl.isl_constraint_set_coefficient_val(
+                    isleq, libisl.isl_dim_set, index, islval)
if equality.constant != 0:
islval = str(equality.constant).encode()
isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
for inequality in inequalities:
-            islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
+            islin = libisl.isl_inequality_alloc(
+                libisl.isl_local_space_copy(islls))
for symbol, coefficient in inequality.coefficients():
islval = str(coefficient).encode()
index = indices[symbol]
-                islin = libisl.isl_constraint_set_coefficient_val(islin,
-                    libisl.isl_dim_set, index, islval)
+                islin = libisl.isl_constraint_set_coefficient_val(
+                    islin, libisl.isl_dim_set, index, islval)
if inequality.constant != 0:
islval = str(inequality.constant).encode()
@@ -321,7 +341,8 @@ class Polyhedron(Domain):
def fromsympy(cls, expression):
domain = Domain.fromsympy(expression)
if not isinstance(domain, Polyhedron):
-            raise ValueError('non-polyhedral expression: {!r}'.format(expression))
+            raise ValueError('non-polyhedral expression: {!r}'.format(
+                expression))
return domain

def tosympy(self):
@@ -388,10 +409,11 @@ def _pseudoconstructor(func):
expression = Rational(expression)
else:
raise TypeError('arguments must be rational numbers '
-                        'or linear expressions')
+                                    'or linear expressions')
return func(*expressions)
return wrapper

+
@_pseudoconstructor
def Lt(*expressions):
"""
@@ -402,6 +424,7 @@ def Lt(*expressions):
inequalities.append(right - left - 1)
return Polyhedron([], inequalities)

+
@_pseudoconstructor
def Le(*expressions):
"""
@@ -412,6 +435,7 @@ def Le(*expressions):
inequalities.append(right - left)
return Polyhedron([], inequalities)

+
@_pseudoconstructor
def Eq(*expressions):
"""
@@ -422,6 +446,7 @@ def Eq(*expressions):
equalities.append(left - right)
return Polyhedron(equalities, [])

+
@_pseudoconstructor
def Ne(*expressions):
"""
@@ -433,6 +458,7 @@ def Ne(*expressions):
domain &= ~Eq(left, right)
return domain

+
@_pseudoconstructor
def Ge(*expressions):
"""
@@ -443,6 +469,7 @@ def Ge(*expressions):
inequalities.append(left - right)
return Polyhedron([], inequalities)

+
@_pseudoconstructor
def Gt(*expressions):
"""