Implement methods Point.__hash__(), Vector.__hash__()

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 787e965..5d9c287 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,12 +1,12 @@
-import ast

 import functools
 import functools

+import math

 import numbers
 import numbers

-import re

 
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl

-from .linexprs import Expression, Constant
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Symbol, Rational

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -32,28 +32,24 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)

-        elif isinstance(equalities, Polyhedron):
+        elif isinstance(equalities, GeometricObject):

             if inequalities is not None:
                 raise TypeError('too many arguments')
             if inequalities is not None:
                 raise TypeError('too many arguments')

-            return equalities
-        elif isinstance(equalities, Domain):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities.polyhedral_hull()
+            return equalities.aspolyhedron()

         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')
         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')

-                equalities[i] = equality._toint()
+                equalities[i] = equality.scaleint()

         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')
         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')

-                inequalities[i] = inequality._toint()
+                inequalities[i] = inequality.scaleint()

         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)


@@ -84,21 +80,41 @@ class Polyhedron(Domain):
         libisl.isl_basic_set_free(islbset)
         return universe
 
         libisl.isl_basic_set_free(islbset)
         return universe
 

-    def polyhedral_hull(self):
+    def aspolyhedron(self):

         return self
 
         return self
 

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        return True
+
+    def subs(self, symbol, expression=None):
+        equalities = [equality.subs(symbol, expression)
+            for equality in self.equalities]
+        inequalities = [inequality.subs(symbol, expression)
+            for inequality in self.inequalities]
+        return Polyhedron(equalities, inequalities)
+

     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         for islconstraint in islconstraints:
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         for islconstraint in islconstraints:

-            islpr = libisl.isl_printer_to_str(mainctx)

             constant = libisl.isl_constraint_get_constant_val(islconstraint)
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             constant = libisl.isl_constraint_get_constant_val(islconstraint)
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}

-            for dim, symbol in enumerate(symbols):
-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, dim)
+            for index, symbol in enumerate(symbols):
+                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
                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient


@@ -119,85 +135,44 @@ class Polyhedron(Domain):
     @classmethod
     def _toislbasicset(cls, equalities, inequalities, symbols):
         dimension = len(symbols)
     @classmethod
     def _toislbasicset(cls, equalities, inequalities, symbols):
         dimension = len(symbols)

+        indices = {symbol: index for index, symbol in enumerate(symbols)}

         islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
         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))
             for symbol, coefficient in equality.coefficients():
         islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
         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))
             for symbol, coefficient in equality.coefficients():

-                val = str(coefficient).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                sid = symbols.index(symbol)
+                islval = str(coefficient).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                index = indices[symbol]

                 isleq = libisl.isl_constraint_set_coefficient_val(isleq,
                 isleq = libisl.isl_constraint_set_coefficient_val(isleq,

-                    libisl.isl_dim_set, sid, val)
+                    libisl.isl_dim_set, index, islval)

             if equality.constant != 0:
             if equality.constant != 0:

-                val = str(equality.constant).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                isleq = libisl.isl_constraint_set_constant_val(isleq, val)
+                islval = str(equality.constant).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                isleq = libisl.isl_constraint_set_constant_val(isleq, islval)

             islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
         for inequality in inequalities:
             islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
             for symbol, coefficient in inequality.coefficients():
             islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
         for inequality in inequalities:
             islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
             for symbol, coefficient in inequality.coefficients():

-                val = str(coefficient).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                sid = symbols.index(symbol)
+                islval = str(coefficient).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                index = indices[symbol]

                 islin = libisl.isl_constraint_set_coefficient_val(islin,
                 islin = libisl.isl_constraint_set_coefficient_val(islin,

-                    libisl.isl_dim_set, sid, val)
+                    libisl.isl_dim_set, index, islval)

             if inequality.constant != 0:
             if inequality.constant != 0:

-                val = str(inequality.constant).encode()
-                val = libisl.isl_val_read_from_str(mainctx, val)
-                islin = libisl.isl_constraint_set_constant_val(islin, val)
+                islval = str(inequality.constant).encode()
+                islval = libisl.isl_val_read_from_str(mainctx, islval)
+                islin = libisl.isl_constraint_set_constant_val(islin, islval)

             islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
         return islbset
 
             islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
         return islbset
 

-    @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):

-        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)
+        domain = Domain.fromstring(string)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(string))
+        return domain

 
     def __repr__(self):
         if self.isempty():
 
     def __repr__(self):
         if self.isempty():


@@ -207,46 +182,20 @@ class Polyhedron(Domain):
         else:
             strings = []
             for equality in self.equalities:
         else:
             strings = []
             for equality in self.equalities:

-                strings.append('Eq({}, 0)'.format(equality))
+                strings.append('0 == {}'.format(equality))

             for inequality in self.inequalities:
             for inequality in self.inequalities:

-                strings.append('Ge({}, 0)'.format(inequality))
+                strings.append('0 <= {}'.format(inequality))

             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 
             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 

-    @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):
     @classmethod
     def fromsympy(cls, expr):

-        import sympy
-        equalities, inequalities = cls._fromsympy(expr)
-        return cls(equalities, inequalities)
+        domain = Domain.fromsympy(expr)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+        return domain

 
     def tosympy(self):
         import sympy
 
     def tosympy(self):
         import sympy


@@ -257,17 +206,92 @@ class Polyhedron(Domain):
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 

+    @classmethod
+    def _sort_polygon_2d(cls, points):
+        if len(points) <= 3:
+            return points
+        o = sum((Vector(point) for point in points)) / len(points)
+        o = Point(o.coordinates())
+        angles = {}
+        for m in points:
+            om = Vector(o, m)
+            dx, dy = (coordinate for symbol, coordinates in om.coordinates())
+            angle = math.atan2(dy, dx)
+            angles[m] = angle
+        return sorted(points, key=angles.get)
+
+    @classmethod
+    def _sort_polygon_3d(cls, points):
+        if len(points) <= 3:
+            return points
+        o = sum((Vector(point) for point in points)) / len(points)
+        o = Point(o.coordinates())
+        a, b = points[:2]
+        oa = Vector(o, a)
+        ob = Vector(o, b)
+        norm_oa = oa.norm()
+        u = (oa.cross(ob)).asunit()
+        angles = {a: 0.}
+        for m in points[1:]:
+            om = Vector(o, m)
+            normprod = norm_oa * om.norm()
+            cosinus = oa.dot(om) / normprod
+            sinus = u.dot(oa.cross(om)) / normprod
+            angle = math.acos(cosinus)
+            angle = math.copysign(angle, sinus)
+            angles[m] = angle
+        return sorted(points, key=angles.get)
+
+    def plot(self):
+        import matplotlib.pyplot as plt
+        from matplotlib.path import Path
+        import matplotlib.patches as patches
+
+        if len(self.symbols)> 3:
+            raise TypeError
+
+        elif len(self.symbols) == 2:
+            verts = self.vertices()
+            points = []
+            codes = [Path.MOVETO]
+            for vert in verts:
+                pairs = ()
+                for sym in sorted(vert, key=Symbol.sortkey):
+                    num = vert.get(sym)
+                    pairs = pairs + (num,)
+                points.append(pairs)
+            points.append((0.0, 0.0))
+            num = len(points)
+            while num > 2:
+                codes.append(Path.LINETO)
+                num = num - 1
+            else:
+                codes.append(Path.CLOSEPOLY)
+            path = Path(points, codes)
+            fig = plt.figure()
+            ax = fig.add_subplot(111)
+            patch = patches.PathPatch(path, facecolor='blue', lw=2)
+            ax.add_patch(patch)
+            ax.set_xlim(-5,5)
+            ax.set_ylim(-5,5)
+            plt.show()
+
+        elif len(self.symbols)==3:
+            return 0
+
+        return points
+

 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):
         if isinstance(left, numbers.Rational):
 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):
         if isinstance(left, numbers.Rational):

-            left = Constant(left)
+            left = Rational(left)

         elif not isinstance(left, Expression):
             raise TypeError('left must be a a rational number '
                 'or a linear expression')
         if isinstance(right, numbers.Rational):
         elif not isinstance(left, Expression):
             raise TypeError('left must be a a rational number '
                 'or a linear expression')
         if isinstance(right, numbers.Rational):

-            right = Constant(right)
+            right = Rational(right)

         elif not isinstance(right, Expression):
             raise TypeError('right must be a a rational number '
                 'or a linear expression')
         elif not isinstance(right, Expression):
             raise TypeError('right must be a a rational number '
                 'or a linear expression')