Use displaystyle in _repr_latex_
[linpy.git] / pypol / domains.py
index a34b75b..5db1856 100644 (file)
@@ -1,8 +1,13 @@
+import ast
 import functools
+import re
 
-from . import islhelper
+from fractions import Fraction
 
-from .islhelper import mainctx, libisl, isl_set_basic_sets
+from . import islhelper
+from .islhelper import mainctx, libisl
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Symbol
 
 
 __all__ = [
@@ -12,7 +17,7 @@ __all__ = [
 
 
 @functools.total_ordering
-class Domain:
+class Domain(GeometricObject):
 
     __slots__ = (
         '_polyhedra',
@@ -23,14 +28,14 @@ class Domain:
     def __new__(cls, *polyhedra):
         from .polyhedra import Polyhedron
         if len(polyhedra) == 1:
-            polyhedron = polyhedra[0]
-            if isinstance(polyhedron, str):
-                return cls.fromstring(polyhedron)
-            elif isinstance(polyhedron, Polyhedron):
-                return polyhedron
+            argument = polyhedra[0]
+            if isinstance(argument, str):
+                return cls.fromstring(argument)
+            elif isinstance(argument, GeometricObject):
+                return argument.aspolyhedron()
             else:
                 raise TypeError('argument must be a string '
-                    'or a Polyhedron instance')
+                    'or a GeometricObject instance')
         else:
             for polyhedron in polyhedra:
                 if not isinstance(polyhedron, Polyhedron):
@@ -47,7 +52,7 @@ class Domain:
         symbols = set()
         for item in iterator:
             symbols.update(item.symbols)
-        return tuple(sorted(symbols))
+        return tuple(sorted(symbols, key=Symbol.sortkey))
 
     @property
     def polyhedra(self):
@@ -62,11 +67,17 @@ class Domain:
         return self._dimension
 
     def disjoint(self):
+        """
+        Returns this set as 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):
+        """
+        Returns true if this set is an Empty set.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
         libisl.isl_set_free(islset)
@@ -76,18 +87,27 @@ class Domain:
         return not self.isempty()
 
     def isuniverse(self):
+        """
+        Returns true if this set is the Universe set.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
         libisl.isl_set_free(islset)
         return universe
 
     def isbounded(self):
+        """
+        Returns true if this set is bounded.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
         libisl.isl_set_free(islset)
         return bounded
 
     def __eq__(self, other):
+        """
+        Returns true if two sets are equal.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
@@ -97,6 +117,9 @@ class Domain:
         return equal
 
     def isdisjoint(self, other):
+        """
+        Return True if two sets have a null intersection.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
@@ -106,6 +129,9 @@ class Domain:
         return equal
 
     def issubset(self, other):
+        """
+        Report whether another set contains this set.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
@@ -115,9 +141,15 @@ class Domain:
         return equal
 
     def __le__(self, other):
+        """
+        Returns true if this set is less than or equal to another set.
+        """
         return self.issubset(other)
 
     def __lt__(self, other):
+        """
+        Returns true if this set is less than another set.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
@@ -127,39 +159,78 @@ class Domain:
         return equal
 
     def complement(self):
+        """
+        Returns the complement of this set.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_complement(islset)
         return self._fromislset(islset, self.symbols)
 
     def __invert__(self):
+        """
+        Returns the complement of this set.
+        """
         return self.complement()
 
     def simplify(self):
-        # see isl_set_coalesce, isl_set_detect_equalities,
-        # isl_set_remove_redundancies
-        # which ones? in which order?
-        raise NotImplementedError
-
-    def polyhedral_hull(self):
-        # several types of hull are available
-        # polyhedral seems to be the more appropriate, to be checked
+        """
+        Returns a set without redundant constraints.
+        """
+        islset = self._toislset(self.polyhedra, self.symbols)
+        islset = libisl.isl_set_remove_redundancies(islset)
+        return self._fromislset(islset, self.symbols)
+
+    def aspolyhedron(self):
+        """
+        Returns polyhedral hull of set.
+        """
         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
         islbset = libisl.isl_set_polyhedral_hull(islset)
         return Polyhedron._fromislbasicset(islbset, self.symbols)
 
-    def project(self, symbols):
-        # not sure what isl_set_project_out actually does…
-        # use isl_set_drop_constraints_involving_dims instead?
-        raise NotImplementedError
+    def asdomain(self):
+        return self
+
+    def project(self, dims):
+        """
+        Return new set with given dimensions removed.
+        """
+        islset = self._toislset(self.polyhedra, self.symbols)
+        n = 0
+        for index, symbol in reversed(list(enumerate(self.symbols))):
+            if symbol in dims:
+                n += 1
+            elif n > 0:
+                islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
+                n = 0
+        if n > 0:
+            islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
+        dims = [symbol for symbol in self.symbols if symbol not in dims]
+        return Domain._fromislset(islset, dims)
 
     def sample(self):
-        from .polyhedra import Polyhedron
+        """
+        Returns a single subset of the input.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
-        islbset = libisl.isl_set_sample(islset)
-        return Polyhedron._fromislbasicset(islbset, self.symbols)
+        islpoint = libisl.isl_set_sample_point(islset)
+        if bool(libisl.isl_point_is_void(islpoint)):
+            libisl.isl_point_free(islpoint)
+            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 = islhelper.isl_val_to_int(coordinate)
+            point[symbol] = coordinate
+        libisl.isl_point_free(islpoint)
+        return point
 
     def intersection(self, *others):
+        """
+         Return the intersection of two sets as a new set.
+        """
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
@@ -170,9 +241,15 @@ class Domain:
         return self._fromislset(islset1, symbols)
 
     def __and__(self, other):
+        """
+         Return the intersection of two sets as a new set.
+        """
         return self.intersection(other)
 
     def union(self, *others):
+        """
+        Return the union of sets as a new set.
+        """
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
@@ -183,12 +260,21 @@ class Domain:
         return self._fromislset(islset1, symbols)
 
     def __or__(self, other):
+        """
+        Return a new set with elements from both sets.
+        """
         return self.union(other)
 
     def __add__(self, other):
+        """
+        Return new set containing all elements in both sets.
+        """
         return self.union(other)
 
     def difference(self, other):
+        """
+        Return the difference of two sets as a new set.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
@@ -196,23 +282,134 @@ class Domain:
         return self._fromislset(islset, symbols)
 
     def __sub__(self, other):
+        """
+        Return the difference of two sets as a new set.
+        """
         return self.difference(other)
 
     def lexmin(self):
+        """
+        Return a new set containing the lexicographic minimum of the elements in the set.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
         return self._fromislset(islset, self.symbols)
 
     def lexmax(self):
+        """
+        Return a new set containing the lexicographic maximum of the elements in the set.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
+    def num_parameters(self):
+        """
+        Return the total number of parameters, input, output or set dimensions.
+        """
+        islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
+        num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
+        return num
+
+    def involves_dims(self, dims):
+        """
+        Returns true if set depends on given dimensions.
+        """
+        islset = self._toislset(self.polyhedra, self.symbols)
+        dims = sorted(dims)
+        symbols = sorted(list(self.symbols))
+        n = 0
+        if len(dims)>0:
+            for dim in dims:
+                if dim in symbols:
+                    first = symbols.index(dims[0])
+                    n +=1
+                else:
+                    first = 0
+        else:
+            return False
+        value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
+        libisl.isl_set_free(islset)
+        return value
+
+    _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+
+    def vertices(self):
+        """
+        Return a list of vertices for this Polygon.
+        """
+        from .polyhedra import Polyhedron
+        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);
+        vertices = islhelper.isl_vertices_vertices(vertices)
+        points = []
+        for vertex in vertices:
+            expr = libisl.isl_vertex_get_expr(vertex)
+            coordinates = []
+            if islhelper.isl_version < '0.13':
+                constraints = islhelper.isl_basic_set_constraints(expr)
+                for constraint in constraints:
+                    constant = libisl.isl_constraint_get_constant_val(constraint)
+                    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 = islhelper.isl_val_to_int(coefficient)
+                        if coefficient != 0:
+                            coordinate = -Fraction(constant, coefficient)
+                            coordinates.append((symbol, coordinate))
+            else:
+
+                # horrible hack, find a cleaner solution
+                string = islhelper.isl_multi_aff_to_str(expr)
+                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)
+                    coordinate = Fraction(numerator, denominator)
+                    coordinates.append((symbol, coordinate))
+            points.append(Point(coordinates))
+        return points
+
+    def points(self):
+        """
+        Returns the points contained in the set.
+        """
+        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):
+                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))
+        return points
+
+    def __contains__(self, point):
+        for polyhedron in self.polyhedra:
+            if point in polyhedron:
+                return True
+        return False
+
+    def subs(self, symbol, expression=None):
+        polyhedra = [polyhedron.subs(symbol, expression)
+            for polyhedron in self.polyhedra]
+        return Domain(*polyhedra)
+
     @classmethod
     def _fromislset(cls, islset, symbols):
         from .polyhedra import Polyhedron
         islset = libisl.isl_set_remove_divs(islset)
-        islbsets = isl_set_basic_sets(islset)
+        islbsets = islhelper.isl_set_basic_sets(islset)
         libisl.isl_set_free(islset)
         polyhedra = []
         for islbset in islbsets:
@@ -230,6 +427,7 @@ class Domain:
             self._dimension = len(self._symbols)
             return self
 
+    @classmethod
     def _toislset(cls, polyhedra, symbols):
         polyhedron = polyhedra[0]
         islbset = polyhedron._toislbasicset(polyhedron.equalities,
@@ -242,24 +440,116 @@ class Domain:
             islset1 = libisl.isl_set_union(islset1, islset2)
         return islset1
 
+    @classmethod
+    def _fromast(cls, node):
+        from .polyhedra import Polyhedron
+        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.UnaryOp):
+            domain = cls._fromast(node.operand)
+            if isinstance(node.operand, ast.invert):
+                return Not(domain)
+        elif isinstance(node, ast.BinOp):
+            domain1 = cls._fromast(node.left)
+            domain2 = cls._fromast(node.right)
+            if isinstance(node.op, ast.BitAnd):
+                return And(domain1, domain2)
+            elif isinstance(node.op, ast.BitOr):
+                return Or(domain1, domain2)
+        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 Polyhedron(equalities, inequalities)
+        raise SyntaxError('invalid syntax')
+
+    _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
+    _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
+    _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
+    _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
+    _RE_NOT = re.compile(r'\bnot\b|!|¬')
+    _RE_NUM_VAR = Expression._RE_NUM_VAR
+    _RE_OPERATORS = re.compile(r'(&|\||~)')
+
     @classmethod
     def fromstring(cls, string):
-        raise NotImplementedError
+        # remove curly brackets
+        string = cls._RE_BRACES.sub(r'', string)
+        # replace '=' by '=='
+        string = cls._RE_EQ.sub(r'\1==\2', string)
+        # 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'
+        string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
+        # add parentheses to force precedence
+        tokens = cls._RE_OPERATORS.split(string)
+        for i, token in enumerate(tokens):
+            if i % 2 == 0:
+                token = '({})'.format(token)
+                tokens[i] = token
+        string = ''.join(tokens)
+        tree = ast.parse(string, 'eval')
+        return cls._fromast(tree)
 
     def __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):
-        raise NotImplementedError
+        import sympy
+        from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
+        funcmap = {
+            sympy.And: And, sympy.Or: Or, sympy.Not: Not,
+            sympy.Lt: Lt, sympy.Le: Le,
+            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 Expression.fromsympy(expr)
+        raise ValueError('non-domain expression: {!r}'.format(expr))
 
     def tosympy(self):
-        raise NotImplementedError
+        import sympy
+        polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
+        return sympy.Or(*polyhedra)
 
 
 def And(*domains):
+    """
+    Return the intersection of two sets as a new set.
+    """
     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe
@@ -267,6 +557,9 @@ def And(*domains):
         return domains[0].intersection(*domains[1:])
 
 def Or(*domains):
+    """
+    Return the union of sets as a new set.
+    """
     if len(domains) == 0:
         from .polyhedra import Empty
         return Empty
@@ -274,4 +567,7 @@ def Or(*domains):
         return domains[0].union(*domains[1:])
 
 def Not(domain):
+    """
+    Returns the complement of this set.
+    """
     return ~domain