Unitary tests for Polyhedron, very incomplete

[linpy.git] / pypol / linear.py

diff --git a/pypol/linear.py b/pypol/linear.py
index 8f73fd3..74b5477 100644 (file)
--- a/pypol/linear.py
+++ b/pypol/linear.py
@@ -1,6 +1,7 @@
-import ctypes, ctypes.util
+import ast

 import functools
 import numbers
 import functools
 import numbers

+import re

 
 from fractions import Fraction, gcd
 
 
 from fractions import Fraction, gcd
 


@@ -12,7 +13,7 @@ __all__ = [
     'Expression', 'Constant', 'Symbol', 'symbols',
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',
     'Expression', 'Constant', 'Symbol', 'symbols',
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',

-    'empty', 'universe'
+    'Empty', 'Universe'

 ]
 
 
 ]
 
 


@@ -49,6 +50,13 @@ class Expression:
     This class implements linear expressions.
     """
 
     This class implements linear expressions.
     """
 

+    __slots__ = (
+        '_coefficients',
+        '_constant',
+        '_symbols',
+        '_dimension',
+    )
+

     def __new__(cls, coefficients=None, constant=0):
         if isinstance(coefficients, str):
             if constant:
     def __new__(cls, coefficients=None, constant=0):
         if isinstance(coefficients, str):
             if constant:


@@ -70,7 +78,7 @@ class Expression:
         self._coefficients = {}
         for symbol, coefficient in coefficients:
             if isinstance(symbol, Symbol):
         self._coefficients = {}
         for symbol, coefficient in coefficients:
             if isinstance(symbol, Symbol):

-                symbol = str(symbol)
+                symbol = symbol.name

             elif not isinstance(symbol, str):
                 raise TypeError('symbols must be strings or Symbol instances')
             if isinstance(coefficient, Constant):
             elif not isinstance(symbol, str):
                 raise TypeError('symbols must be strings or Symbol instances')
             if isinstance(coefficient, Constant):


@@ -87,9 +95,36 @@ class Expression:
         self._dimension = len(self._symbols)
         return self
 
         self._dimension = len(self._symbols)
         return self
 

+    @classmethod
+    def _fromast(cls, node):
+        if isinstance(node, ast.Module) and len(node.body) == 1:
+            return cls._fromast(node.body[0])
+        elif isinstance(node, ast.Expr):
+            return cls._fromast(node.value)
+        elif isinstance(node, ast.Name):
+            return Symbol(node.id)
+        elif isinstance(node, ast.Num):
+            return Constant(node.n)
+        elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
+            return -cls._fromast(node.operand)
+        elif isinstance(node, ast.BinOp):
+            left = cls._fromast(node.left)
+            right = cls._fromast(node.right)
+            if isinstance(node.op, ast.Add):
+                return left + right
+            elif isinstance(node.op, ast.Sub):
+                return left - right
+            elif isinstance(node.op, ast.Mult):
+                return left * right
+            elif isinstance(node.op, ast.Div):
+                return left / right
+        raise SyntaxError('invalid syntax')
+

     @classmethod
     def fromstring(cls, string):
     @classmethod
     def fromstring(cls, string):

-        raise NotImplementedError
+        string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+        tree = ast.parse(string, 'eval')
+        return cls._fromast(tree)

 
     @property
     def symbols(self):
 
     @property
     def symbols(self):


@@ -127,15 +162,11 @@ class Expression:
             yield self.coefficient(symbol)
         yield self.constant
 
             yield self.coefficient(symbol)
         yield self.constant
 

-    @property
-    def symbol(self):
-        raise ValueError('not a symbol: {}'.format(self))
-

     def issymbol(self):
         return False
 
     def __bool__(self):
     def issymbol(self):
         return False
 
     def __bool__(self):

-        True
+        return True

 
     def __pos__(self):
         return self
 
     def __pos__(self):
         return self


@@ -271,7 +302,7 @@ class Expression:
                 self.constant == other.constant
 
     def __hash__(self):
                 self.constant == other.constant
 
     def __hash__(self):

-        return hash((self._coefficients, self._constant))
+        return hash((tuple(sorted(self._coefficients.items())), self._constant))

 
     def _toint(self):
         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
 
     def _toint(self):
         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),


@@ -298,6 +329,31 @@ class Expression:
     def __gt__(self, other):
         return Polyhedron(inequalities=[(self - other)._toint() - 1])
 
     def __gt__(self, other):
         return Polyhedron(inequalities=[(self - other)._toint() - 1])
 

+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        coefficients = {}
+        constant = 0
+        for symbol, coefficient in expr.as_coefficients_dict().items():
+            coefficient = Fraction(coefficient.p, coefficient.q)
+            if symbol == sympy.S.One:
+                constant = coefficient
+            elif isinstance(symbol, sympy.Symbol):
+                symbol = symbol.name
+                coefficients[symbol] = coefficient
+            else:
+                raise ValueError('non-linear expression: {!r}'.format(expr))
+        return cls(coefficients, constant)
+
+    def tosympy(self):
+        import sympy
+        expr = 0
+        for symbol, coefficient in self.coefficients():
+            term = coefficient * sympy.Symbol(symbol)
+            expr += term
+        expr += self.constant
+        return expr
+

 
 class Constant(Expression):
 
 
 class Constant(Expression):
 


@@ -324,59 +380,86 @@ class Constant(Expression):
         return bool(self.constant)
 
     def __repr__(self):
         return bool(self.constant)
 
     def __repr__(self):

-        return '{}({!r})'.format(self.__class__.__name__, self._constant)
+        if self.constant.denominator == 1:
+            return '{}({!r})'.format(self.__class__.__name__, self.constant)
+        else:
+            return '{}({!r}, {!r})'.format(self.__class__.__name__,
+                self.constant.numerator, self.constant.denominator)
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        if isinstance(expr, sympy.Rational):
+            return cls(expr.p, expr.q)
+        elif isinstance(expr, numbers.Rational):
+            return cls(expr)
+        else:
+            raise TypeError('expr must be a sympy.Rational instance')

 
 
 class Symbol(Expression):
 
 
 
 class Symbol(Expression):
 

+    __slots__ = Expression.__slots__ + (
+        '_name',
+    )
+

     def __new__(cls, name):
         if isinstance(name, Symbol):
     def __new__(cls, name):
         if isinstance(name, Symbol):

-            name = name.symbol
+            name = name.name

         elif not isinstance(name, str):
             raise TypeError('name must be a string or a Symbol instance')
         self = object().__new__(cls)
         self._coefficients = {name: 1}
         self._constant = 0
         self._symbols = tuple(name)
         elif not isinstance(name, str):
             raise TypeError('name must be a string or a Symbol instance')
         self = object().__new__(cls)
         self._coefficients = {name: 1}
         self._constant = 0
         self._symbols = tuple(name)

-        self._symbol = name
+        self._name = name

         self._dimension = 1
         return self
 
     @property
         self._dimension = 1
         return self
 
     @property

-    def symbol(self):
-        return self._symbol
+    def name(self):
+        return self._name

 
     def issymbol(self):
         return True
 
     def __repr__(self):
 
     def issymbol(self):
         return True
 
     def __repr__(self):

-        return '{}({!r})'.format(self.__class__.__name__, self._symbol)
+        return '{}({!r})'.format(self.__class__.__name__, self._name)
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        if isinstance(expr, sympy.Symbol):
+            return cls(expr.name)
+        else:
+            raise TypeError('expr must be a sympy.Symbol instance')
+

 
 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()
 
 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()

-    return (symbol(name) for name in names)
+    return (Symbol(name) for name in names)

 
 
 @_polymorphic_operator
 def eq(a, b):
 
 
 @_polymorphic_operator
 def eq(a, b):

-    return a._eq(b)
+    return a.__eq__(b)

 
 @_polymorphic_operator
 def le(a, b):
 
 @_polymorphic_operator
 def le(a, b):

-    return a <= b
+    return a.__le__(b)

 
 @_polymorphic_operator
 def lt(a, b):
 
 @_polymorphic_operator
 def lt(a, b):

-    return a < b
+    return a.__lt__(b)

 
 @_polymorphic_operator
 def ge(a, b):
 
 @_polymorphic_operator
 def ge(a, b):

-    return a >= b
+    return a.__ge__(b)

 
 @_polymorphic_operator
 def gt(a, b):
 
 @_polymorphic_operator
 def gt(a, b):

-    return a > b
+    return a.__gt__(b)

 
 
 class Polyhedron:
 
 
 class Polyhedron:


@@ -384,6 +467,13 @@ class Polyhedron:
     This class implements polyhedrons.
     """
 
     This class implements polyhedrons.
     """
 

+    __slots__ = (
+        '_equalities',
+        '_inequalities',
+        '_constraints',
+        '_symbols',
+    )
+

     def __new__(cls, equalities=None, inequalities=None):
         if isinstance(equalities, str):
             if inequalities is not None:
     def __new__(cls, equalities=None, inequalities=None):
         if isinstance(equalities, str):
             if inequalities is not None:


@@ -415,9 +505,54 @@ class Polyhedron:
         self._symbols = tuple(sorted(self._symbols))
         return self
 
         self._symbols = tuple(sorted(self._symbols))
         return self
 

+    @classmethod
+    def _fromast(cls, node):
+        if isinstance(node, ast.Module) and len(node.body) == 1:
+            return cls._fromast(node.body[0])
+        elif isinstance(node, ast.Expr):
+            return cls._fromast(node.value)
+        elif isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitAnd):
+            equalities1, inequalities1 = cls._fromast(node.left)
+            equalities2, inequalities2 = cls._fromast(node.right)
+            equalities = equalities1 + equalities2
+            inequalities = inequalities1 + inequalities2
+            return equalities, inequalities
+        elif isinstance(node, ast.Compare):
+            equalities = []
+            inequalities = []
+            left = Expression._fromast(node.left)
+            for i in range(len(node.ops)):
+                op = node.ops[i]
+                right = Expression._fromast(node.comparators[i])
+                if isinstance(op, ast.Lt):
+                    inequalities.append(right - left - 1)
+                elif isinstance(op, ast.LtE):
+                    inequalities.append(right - left)
+                elif isinstance(op, ast.Eq):
+                    equalities.append(left - right)
+                elif isinstance(op, ast.GtE):
+                    inequalities.append(left - right)
+                elif isinstance(op, ast.Gt):
+                    inequalities.append(left - right - 1)
+                else:
+                    break
+                left = right
+            else:
+                return equalities, inequalities
+        raise SyntaxError('invalid syntax')
+

     @classmethod
     def fromstring(cls, string):
     @classmethod
     def fromstring(cls, string):

-        raise NotImplementedError
+        string = string.strip()
+        string = re.sub(r'^\{\s*|\s*\}$', '', string)
+        string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
+        string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+        tokens = re.split(r',|;|and|&&|/\\|∧', string, flags=re.I)
+        tokens = ['({})'.format(token) for token in tokens]
+        string = ' & '.join(tokens)
+        tree = ast.parse(string, 'eval')
+        equalities, inequalities = cls._fromast(tree)
+        return cls(equalities, inequalities)

 
     @property
     def equalities(self):
 
     @property
     def equalities(self):


@@ -447,27 +582,42 @@ class Polyhedron:
         raise NotImplementedError
 
     def __eq__(self, other):
         raise NotImplementedError
 
     def __eq__(self, other):

-        raise NotImplementedError
+        # works correctly when symbols is not passed
+        # should be equal if values are the same even if symbols are different
+        bset = self._toisl()
+        other = other._toisl()
+        return bool(libisl.isl_basic_set_plain_is_equal(bset, other))

 
     def isempty(self):
         bset = self._toisl()
         return bool(libisl.isl_basic_set_is_empty(bset))
 
     def isuniverse(self):
 
     def isempty(self):
         bset = self._toisl()
         return bool(libisl.isl_basic_set_is_empty(bset))
 
     def isuniverse(self):

-        raise NotImplementedError
+        bset = self._toisl()
+        return bool(libisl.isl_basic_set_is_universe(bset))

 
     def isdisjoint(self, other):
         # return true if the polyhedron has no elements in common with other
 
     def isdisjoint(self, other):
         # return true if the polyhedron has no elements in common with other

-        raise NotImplementedError
+        #symbols = self._symbolunion(other)
+        bset = self._toisl()
+        other = other._toisl()
+        return bool(libisl.isl_set_is_disjoint(bset, other))

 
     def issubset(self, other):
 
     def issubset(self, other):

-        raise NotImplementedError
+        # check if self(bset) is a subset of other
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        return bool(libisl.isl_set_is_strict_subset(other, bset))

 
     def __le__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):
 
     def __le__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):

-        raise NotImplementedError
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        return bool(libisl.isl_set_is_strict_subset(other, bset))

 
     def issuperset(self, other):
         # test whether every element in other is in the polyhedron
 
     def issuperset(self, other):
         # test whether every element in other is in the polyhedron


@@ -477,6 +627,10 @@ class Polyhedron:
         return self.issuperset(other)
 
     def __gt__(self, other):
         return self.issuperset(other)
 
     def __gt__(self, other):

+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        bool(libisl.isl_set_is_strict_subset(other, bset))

         raise NotImplementedError
 
     def union(self, *others):
         raise NotImplementedError
 
     def union(self, *others):


@@ -502,10 +656,13 @@ class Polyhedron:
     def __and__(self, other):
         return self.intersection(other)
 
     def __and__(self, other):
         return self.intersection(other)
 

-    def difference(self, *others):
-        # return a new polyhedron with elements in the polyhedron that are not
-        # in the others
-        raise NotImplementedError
+    def difference(self, other):
+        # return a new polyhedron with elements in the polyhedron that are not in the other
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        difference = libisl.isl_set_subtract(bset, other)
+        return difference

 
     def __sub__(self, other):
         return self.difference(other)
 
     def __sub__(self, other):
         return self.difference(other)


@@ -519,10 +676,57 @@ class Polyhedron:
         return '{{{}}}'.format(', '.join(constraints))
 
     def __repr__(self):
         return '{{{}}}'.format(', '.join(constraints))
 
     def __repr__(self):

-        equalities = list(self.equalities)
-        inequalities = list(self.inequalities)
-        return '{}(equalities={!r}, inequalities={!r})' \
-                ''.format(self.__class__.__name__, equalities, inequalities)
+        if self.isempty():
+            return 'Empty'
+        elif self.isuniverse():
+            return 'Universe'
+        else:
+            equalities = list(self.equalities)
+            inequalities = list(self.inequalities)
+            return '{}(equalities={!r}, inequalities={!r})' \
+                    ''.format(self.__class__.__name__, equalities, inequalities)
+
+    @classmethod
+    def _fromsympy(cls, expr):
+        import sympy
+        equalities = []
+        inequalities = []
+        if expr.func == sympy.And:
+            for arg in expr.args:
+                arg_eqs, arg_ins = cls._fromsympy(arg)
+                equalities.extend(arg_eqs)
+                inequalities.extend(arg_ins)
+        elif expr.func == sympy.Eq:
+            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+            equalities.append(expr)
+        else:
+            if expr.func == sympy.Lt:
+                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
+            elif expr.func == sympy.Le:
+                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
+            elif expr.func == sympy.Ge:
+                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+            elif expr.func == sympy.Gt:
+                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
+            else:
+                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+            inequalities.append(expr)
+        return equalities, inequalities
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        equalities, inequalities = cls._fromsympy(expr)
+        return cls(equalities, inequalities)
+
+    def tosympy(self):
+        import sympy
+        constraints = []
+        for equality in self.equalities:
+            constraints.append(sympy.Eq(equality.tosympy(), 0))
+        for inequality in self.inequalities:
+            constraints.append(sympy.Ge(inequality.tosympy(), 0))
+        return sympy.And(*constraints)

 
     def _symbolunion(self, *others):
         symbols = set(self.symbols)
 
     def _symbolunion(self, *others):
         symbols = set(self.symbols)


@@ -533,40 +737,39 @@ class Polyhedron:
     def _toisl(self, symbols=None):
         if symbols is None:
             symbols = self.symbols
     def _toisl(self, symbols=None):
         if symbols is None:
             symbols = self.symbols

-        num_coefficients = len(symbols)
-        space = libisl.isl_space_set_alloc(_main_ctx, 0, num_coefficients)
+        dimension = len(symbols)
+        space = libisl.isl_space_set_alloc(_main_ctx, 0, dimension)

         bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
         ls = libisl.isl_local_space_from_space(space)
         bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
         ls = libisl.isl_local_space_from_space(space)

-        ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
-        cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
-        '''if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set'''
-        if list(self.equalities): #check if any equalities exist
-            for eq in self.equalities:
-                coeff_eq = dict(eq.coefficients())
-                if eq.constant:
-                    value = eq.constant
-                    ceq = libisl.isl_constraint_set_constant_si(ceq, value)
-                for eq in coeff_eq:
-                    num = coeff_eq.get(eq)
-                    iden = symbols.index(eq)
-                    ceq = libisl.isl_constraint_set_coefficient_si(ceq, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
+        for equality in self.equalities:
+            ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
+            for symbol, coefficient in equality.coefficients():
+                val = str(coefficient).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                dim = symbols.index(symbol)
+                ceq = libisl.isl_constraint_set_coefficient_val(ceq, libisl.isl_dim_set, dim, val)
+            if equality.constant != 0:
+                val = str(equality.constant).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                ceq = libisl.isl_constraint_set_constant_val(ceq, val)

             bset = libisl.isl_basic_set_add_constraint(bset, ceq)
             bset = libisl.isl_basic_set_add_constraint(bset, ceq)

-        if list(self.inequalities): #check if any inequalities exist
-            for ineq in self.inequalities:
-                coeff_in = dict(ineq.coefficients())
-                if ineq.constant:
-                    value = ineq.constant
-                    cin = libisl.isl_constraint_set_constant_si(cin, value)
-                for ineq in coeff_in:
-                    num = coeff_in.get(ineq)
-                    iden = symbols.index(ineq)
-                    cin = libisl.isl_constraint_set_coefficient_si(cin, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
+        for inequality in self.inequalities:
+            cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
+            for symbol, coefficient in inequality.coefficients():
+                val = str(coefficient).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                dim = symbols.index(symbol)
+                cin = libisl.isl_constraint_set_coefficient_val(cin, libisl.isl_dim_set, dim, val)
+            if inequality.constant != 0:
+                val = str(inequality.constant).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                cin = libisl.isl_constraint_set_constant_val(cin, val)

             bset = libisl.isl_basic_set_add_constraint(bset, cin)
         bset = isl.BasicSet(bset)
         return bset
 
     @classmethod
             bset = libisl.isl_basic_set_add_constraint(bset, cin)
         bset = isl.BasicSet(bset)
         return bset
 
     @classmethod

-    def _fromisl(cls, bset):
+    def _fromisl(cls, bset, symbols):

         raise NotImplementedError
         equalities = ...
         inequalities = ...
         raise NotImplementedError
         equalities = ...
         inequalities = ...


@@ -575,24 +778,16 @@ class Polyhedron:
         isl example code gives isl form as:
             "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
             our printer is giving form as:
         isl example code gives isl form as:
             "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
             our printer is giving form as:

-            b'{ [i0] : 1 = 0 }' '''
-        #bset = self
-        # if self._equalities:
-        #     constraints = libisl.isl_basic_set_equalities_matrix(bset, 3)
-        # elif self._inequalities:
-        #     constraints = libisl.isl_basic_set_inequalities_matrix(bset, 3)
-        # print(constraints)
-        # return constraints
+            { [i0, i1] : 2i1 >= -2 - i0 } '''
+
+Empty = eq(0,1)

 
 

-empty = None #eq(0,1)
-universe = None #Polyhedron()
+Universe = Polyhedron()

 
 
 if __name__ == '__main__':
 
 
 if __name__ == '__main__':

-    ex1 = Expression(coefficients={'a': 1, 'x': 2}, constant=2)
-    ex2 = Expression(coefficients={'a': 3  , 'b': 2}, constant=3)
-    p = Polyhedron(inequalities=[ex1, ex2])
-    bs = p._toisl()
-    print(bs)
-    print('empty ?', p.isempty())
-    print('empty ?', eq(0, 1).isempty())
+    #p = Polyhedron('2a + 2b + 1 == 0') # empty
+    p = Polyhedron('3x + 2y + 3 == 0, y == 0') # not empty
+    ip = p._toisl()
+    print(ip)
+    print(ip.constraints())