Improve readability of Polyhedron.__repr__()
[linpy.git] / linpy / polyhedra.py
index b486be1..bfc7efe 100644 (file)
@@ -44,7 +44,6 @@ class Polyhedron(Domain):
     __slots__ = (
         '_equalities',
         '_inequalities',
-        '_constraints',
         '_symbols',
         '_dimension',
     )
@@ -88,22 +87,20 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()
-        if equalities is None:
-            equalities = []
-        else:
-            for i, equality in enumerate(equalities):
+        sc_equalities = []
+        if equalities is not None:
+            for equality in equalities:
                 if not isinstance(equality, LinExpr):
                     raise TypeError('equalities must be linear expressions')
-                equalities[i] = equality.scaleint()
-        if inequalities is None:
-            inequalities = []
-        else:
-            for i, inequality in enumerate(inequalities):
+                sc_equalities.append(equality.scaleint())
+        sc_inequalities = []
+        if inequalities is not None:
+            for inequality in inequalities:
                 if not isinstance(inequality, LinExpr):
                     raise TypeError('inequalities must be linear expressions')
-                inequalities[i] = inequality.scaleint()
-        symbols = cls._xsymbols(equalities + inequalities)
-        islbset = cls._toislbasicset(equalities, inequalities, symbols)
+                sc_inequalities.append(inequality.scaleint())
+        symbols = cls._xsymbols(sc_equalities + sc_inequalities)
+        islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
 
     @property
@@ -128,7 +125,7 @@ class Polyhedron(Domain):
         The tuple of constraints, i.e., equalities and inequalities. This is
         semantically equivalent to: equalities + inequalities.
         """
-        return self._constraints
+        return self._equalities + self._inequalities
 
     @property
     def polyhedra(self):
@@ -147,6 +144,15 @@ class Polyhedron(Domain):
     def aspolyhedron(self):
         return self
 
+    def convex_union(self, *others):
+        """
+        Return the convex union of two or more polyhedra.
+        """
+        for other in others:
+            if not isinstance(other, Polyhedron):
+                raise TypeError('arguments must be Polyhedron instances')
+        return Polyhedron(self.union(*others))
+
     def __contains__(self, point):
         if not isinstance(point, Point):
             raise TypeError('point must be a Point instance')
@@ -167,7 +173,11 @@ class Polyhedron(Domain):
             for inequality in self.inequalities]
         return Polyhedron(equalities, inequalities)
 
-    def _asinequalities(self):
+    def asinequalities(self):
+        """
+        Express the polyhedron using inequalities, given as a list of
+        expressions greater or equal to 0.
+        """
         inequalities = list(self.equalities)
         inequalities.extend([-expression for expression in self.equalities])
         inequalities.extend(self.inequalities)
@@ -176,11 +186,14 @@ class Polyhedron(Domain):
     def widen(self, other):
         """
         Compute the standard widening of two polyhedra, à la Halbwachs.
+
+        In its current implementation, this method is slow and should not be
+        used on large polyhedra.
         """
         if not isinstance(other, Polyhedron):
-            raise ValueError('argument must be a Polyhedron instance')
-        inequalities1 = self._asinequalities()
-        inequalities2 = other._asinequalities()
+            raise TypeError('argument must be a Polyhedron instance')
+        inequalities1 = self.asinequalities()
+        inequalities2 = other.asinequalities()
         inequalities = []
         for inequality1 in inequalities1:
             if other <= Polyhedron(inequalities=[inequality1]):
@@ -219,8 +232,7 @@ class Polyhedron(Domain):
         self = object().__new__(Polyhedron)
         self._equalities = tuple(equalities)
         self._inequalities = tuple(inequalities)
-        self._constraints = tuple(equalities + inequalities)
-        self._symbols = cls._xsymbols(self._constraints)
+        self._symbols = cls._xsymbols(self.constraints)
         self._dimension = len(self._symbols)
         return self
 
@@ -269,9 +281,33 @@ class Polyhedron(Domain):
     def __repr__(self):
         strings = []
         for equality in self.equalities:
-            strings.append('Eq({}, 0)'.format(equality))
+            left, right, swap = 0, 0, False
+            for i, (symbol, coefficient) in enumerate(equality.coefficients()):
+                if coefficient > 0:
+                    left += coefficient * symbol
+                else:
+                    right -= coefficient * symbol
+                    if i == 0:
+                        swap = True
+            if equality.constant > 0:
+                left += equality.constant
+            else:
+                right -= equality.constant
+            if swap:
+                left, right = right, left
+            strings.append('{} == {}'.format(left, right))
         for inequality in self.inequalities:
-            strings.append('Ge({}, 0)'.format(inequality))
+            left, right = 0, 0
+            for symbol, coefficient in inequality.coefficients():
+                if coefficient < 0:
+                    left -= coefficient * symbol
+                else:
+                    right += coefficient * symbol
+            if inequality.constant < 0:
+                left -= inequality.constant
+            else:
+                right += inequality.constant
+            strings.append('{} <= {}'.format(left, right))
         if len(strings) == 1:
             return strings[0]
         else:
@@ -307,13 +343,10 @@ class EmptyType(Polyhedron):
     The empty polyhedron, whose set of constraints is not satisfiable.
     """
 
-    __slots__ = Polyhedron.__slots__
-
     def __new__(cls):
         self = object().__new__(cls)
         self._equalities = (Rational(1),)
         self._inequalities = ()
-        self._constraints = self._equalities
         self._symbols = ()
         self._dimension = 0
         return self
@@ -338,13 +371,10 @@ class UniverseType(Polyhedron):
     i.e. is empty.
     """
 
-    __slots__ = Polyhedron.__slots__
-
     def __new__(cls):
         self = object().__new__(cls)
         self._equalities = ()
         self._inequalities = ()
-        self._constraints = ()
         self._symbols = ()
         self._dimension = ()
         return self
@@ -358,63 +388,77 @@ class UniverseType(Polyhedron):
 Universe = UniverseType()
 
 
-def _polymorphic(func):
+def _pseudoconstructor(func):
     @functools.wraps(func)
-    def wrapper(left, right):
-        if not isinstance(left, LinExpr):
-            if isinstance(left, numbers.Rational):
-                left = Rational(left)
-            else:
-                raise TypeError('left must be a a rational number '
-                    'or a linear expression')
-        if not isinstance(right, LinExpr):
-            if isinstance(right, numbers.Rational):
-                right = Rational(right)
-            else:
-                raise TypeError('right must be a a rational number '
-                    'or a linear expression')
-        return func(left, right)
+    def wrapper(expr1, expr2, *exprs):
+        exprs = (expr1, expr2) + exprs
+        for expr in exprs:
+            if not isinstance(expr, LinExpr):
+                if isinstance(expr, numbers.Rational):
+                    expr = Rational(expr)
+                else:
+                    raise TypeError('arguments must be rational numbers '
+                        'or linear expressions')
+        return func(*exprs)
     return wrapper
 
-@_polymorphic
-def Lt(left, right):
+@_pseudoconstructor
+def Lt(*exprs):
     """
     Create the polyhedron with constraints expr1 < expr2 < expr3 ...
     """
-    return Polyhedron([], [right - left - 1])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(right - left - 1)
+    return Polyhedron([], inequalities)
 
-@_polymorphic
-def Le(left, right):
+@_pseudoconstructor
+def Le(*exprs):
     """
     Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
     """
-    return Polyhedron([], [right - left])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(right - left)
+    return Polyhedron([], inequalities)
 
-@_polymorphic
-def Eq(left, right):
+@_pseudoconstructor
+def Eq(*exprs):
     """
     Create the polyhedron with constraints expr1 == expr2 == expr3 ...
     """
-    return Polyhedron([left - right], [])
+    equalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        equalities.append(left - right)
+    return Polyhedron(equalities, [])
 
-@_polymorphic
-def Ne(left, right):
+@_pseudoconstructor
+def Ne(*exprs):
     """
     Create the domain such that expr1 != expr2 != expr3 ... The result is a
-    Domain, not a Polyhedron.
+    Domain object, not a Polyhedron.
     """
-    return ~Eq(left, right)
+    domain = Universe
+    for left, right in zip(exprs, exprs[1:]):
+        domain &= ~Eq(left, right)
+    return domain
 
-@_polymorphic
-def Gt(left, right):
+@_pseudoconstructor
+def Ge(*exprs):
     """
-    Create the polyhedron with constraints expr1 > expr2 > expr3 ...
+    Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
     """
-    return Polyhedron([], [left - right - 1])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(left - right)
+    return Polyhedron([], inequalities)
 
-@_polymorphic
-def Ge(left, right):
+@_pseudoconstructor
+def Gt(*exprs):
     """
-    Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
+    Create the polyhedron with constraints expr1 > expr2 > expr3 ...
     """
-    return Polyhedron([], [left - right])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(left - right - 1)
+    return Polyhedron([], inequalities)