linpy/tests/test_domains.py

   1 # Copyright 2014 MINES ParisTech
   2 #
   3 # This file is part of LinPy.
   4 #
   5 # LinPy is free software: you can redistribute it and/or modify
   6 # it under the terms of the GNU General Public License as published by
   7 # the Free Software Foundation, either version 3 of the License, or
   8 # (at your option) any later version.
   9 #
  10 # LinPy is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13 # GNU General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU General Public License
  16 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
  17
  18 import unittest
  19
  20 from ..domains import And, Or
  21 from ..linexprs import Symbol, symbols
  22 from ..polyhedra import Empty, Eq, Ge, Polyhedron
  23
  24
  25 class TestDomain(unittest.TestCase):
  26
  27     def setUp(self):
  28         x, y = symbols('x y')
  29         self.square1 = Polyhedron(inequalities=[x, 2 - x, y, 2 - y])
  30         self.square2 = Polyhedron(inequalities=[x - 1, 3 - x, y - 1, 3 - y])
  31         self.square3 = Polyhedron(inequalities=[x, 3 - x, y, 3 - y])
  32         self.square4 = Polyhedron(inequalities=[x - 1, 2 - x, y - 1, 2 - y])
  33         self.square5 = Polyhedron(inequalities=[x - 3, 6 - x, y - 3, 6 - y])
  34         self.square6 = Polyhedron(equalities=[3 - y],
  35                                   inequalities=[x - 1, 3 - x, y - 1])
  36         self.unbound_poly = Polyhedron(inequalities=[x, 3 - x, y])
  37         self.universe = Polyhedron([])
  38         self.empty = Empty
  39         self.disjoint = And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
  40         self.complement = Or(Ge(-x - 1, 0), Ge(x - 3, 0),
  41                              And(Ge(x, 0), Ge(-x + 2, 0), Ge(-y - 1, 0)),
  42                              And(Ge(x, 0), Ge(-x + 2, 0), Ge(y - 3, 0)))
  43         self.hull = And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
  44         self.dropped = And(Ge(y, 0), Ge(-y + 2, 0))
  45         self.intersection = And(Ge(x - 1, 0), Ge(-x + 2, 0), Ge(y - 1, 0),
  46                                 Ge(-y + 2, 0))
  47         self.union = Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)),
  48                         And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0),
  49                             Ge(-y + 3, 0)))
  50         self.sum1 = Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)),
  51                        And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0),
  52                            Ge(-y + 3, 0)))
  53         self.sum2 = And(Ge(x, 0), Ge(y, 0), Ge(-y + 3, 0), Ge(-x + 3, 0),
  54                         Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
  55         self.difference1 = Or(And(Eq(x - 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)),
  56                               And(Eq(y - 3, 0), Ge(x - 1, 0), Ge(-x + 2, 0)))
  57         self.difference2 = And(Ge(x + y - 4, 0), Ge(-x + 3, 0), Ge(-y + 3, 0))
  58         self.lexmin = And(Eq(y, 0), Eq(x, 0))
  59         self.lexmax = And(Eq(y - 2, 0), Eq(x - 2, 0))
  60
  61     def test_new(self):
  62         with self.assertRaises(TypeError):
  63             Polyhedron(1)
  64
  65     def test_disjoint(self):
  66         self.assertEqual(self.square1.make_disjoint(), self.disjoint)
  67         self.assertEqual(self.empty.make_disjoint(), Empty)
  68         self.assertEqual(self.universe.make_disjoint(), self.universe)
  69
  70     def test_isempty(self):
  71         self.assertFalse(self.square1.isempty())
  72         self.assertTrue(self.empty.isempty())
  73         self.assertFalse(self.universe.isempty())
  74
  75     def test_isuniverse(self):
  76         self.assertFalse(self.square1.isuniverse())
  77         self.assertTrue(self.universe.isuniverse())
  78
  79     def test_isbounded(self):
  80         self.assertTrue(self.square1.isbounded())
  81         self.assertFalse(self.unbound_poly.isbounded())
  82
  83     def test_eq(self):
  84         self.assertTrue(self.square1 == self.square1)
  85         self.assertFalse(self.square1 == self.square2)
  86         self.assertFalse(self.empty == self.universe)
  87
  88     def test_isdisjoint(self):
  89         self.assertFalse(self.square1.isdisjoint(self.square2))
  90         self.assertFalse(self.universe.isdisjoint(self.square1))
  91         self.assertTrue(self.square1.isdisjoint(self.square5))
  92         self.assertTrue(self.empty.isdisjoint(self.square1))
  93
  94     def test_issubset(self):
  95         self.assertTrue(self.square4.issubset(self.unbound_poly))
  96         self.assertFalse(self.square1.issubset(self.square2))
  97         self.assertTrue(self.square1.issubset(self.universe))
  98         self.assertTrue(self.empty.issubset(self.square1))
  99
 100     def test_le(self):
 101         self.assertTrue(self.square4 <= self.square3)
 102         self.assertFalse(self.square3 <= self.square4)
 103         self.assertTrue(self.empty <= self.square1)
 104         self.assertTrue(self.square1 <= self.universe)
 105
 106     def test_lt(self):
 107         self.assertTrue(self.square4 < self.square3)
 108         self.assertFalse(self.square3 < self.square4)
 109         self.assertTrue(self.empty < self.square1)
 110         self.assertTrue(self.square1 < self.universe)
 111
 112     def test_complement(self):
 113         self.assertEqual(~self.square1, self.complement)
 114         self.assertEqual(~self.universe, Empty)
 115         self.assertEqual(~self.empty, self.universe)
 116
 117     def test_aspolyhedron(self):
 118         self.assertEqual(self.square1.aspolyhedron(), self.hull)
 119         self.assertEqual(self.universe.aspolyhedron(), self.universe)
 120         self.assertEqual(self.empty.aspolyhedron(), self.empty)
 121
 122     def test_project(self):
 123         self.assertEqual(self.square1.project(symbols('x')), self.dropped)
 124         self.assertEqual(self.square1.project(symbols('x y')), self.universe)
 125         self.assertEqual(self.universe.project([]), self.universe)
 126         self.assertEqual(self.empty.project([]), Empty)
 127
 128     def test_sample(self):
 129         self.assertEqual(self.square6.sample(),
 130                          {Symbol('x'): 1, Symbol('y'): 3})
 131         with self.assertRaises(ValueError):
 132             self.empty.sample()
 133         self.assertEqual(self.universe.sample(), {})
 134
 135     def test_intersection(self):
 136         self.assertEqual(self.square1.intersection(self.square2),
 137                          self.intersection)
 138
 139     def test_and(self):
 140         self.assertEqual(self.square2 & self.square1, self.intersection)
 141         self.assertEqual(self.square1 & self.universe, self.square1)
 142         self.assertEqual(self.empty & self.square1, Empty)
 143         self.assertEqual(self.universe & self.universe, self.universe)
 144         self.assertEqual(self.universe & self.empty, Empty)
 145         self.assertEqual(self.empty & self.empty, Empty)
 146
 147     def test_union(self):
 148         self.assertEqual(self.square1.union(self.square2), self.union)
 149         self.assertEqual(self.square1.union(self.empty), self.square1)
 150         self.assertEqual(self.square1.union(self.universe), self.universe)
 151         self.assertEqual(self.universe.union(self.universe), self.universe)
 152         self.assertEqual(self.empty.union(self.empty), self.empty)
 153
 154     def test_or(self):
 155         self.assertEqual(self.square1 | self.square2, self.union)
 156
 157     def test_add(self):
 158         self.assertEqual(self.square2 + self.square1, self.sum1)
 159         self.assertEqual(Polyhedron(self.square1 + self.square2), self.sum2)
 160         self.assertEqual(self.universe + self.square1, self.universe)
 161         self.assertEqual(self.empty + self.square1, self.square1)
 162         self.assertEqual(self.universe + self.universe, self.universe)
 163
 164     def test_difference(self):
 165         self.assertEqual(self.square2 - self.square1, self.difference1)
 166         self.assertEqual(Polyhedron(self.square2 - self.square1),
 167                          self.difference2)
 168         self.assertEqual(self.square2 - self.square2, Empty)
 169         self.assertEqual(self.universe - self.universe, Empty)
 170
 171     def test_lexmin(self):
 172         self.assertEqual(self.square1.lexmin(), self.lexmin)
 173         self.assertEqual(self.universe.lexmin(), self.universe)
 174         self.assertEqual(self.empty.lexmin(), Empty)
 175
 176     def test_lexmax(self):
 177         self.assertEqual(self.square1.lexmax(), self.lexmax)
 178         self.assertEqual(self.universe.lexmax(), self.universe)
 179         self.assertEqual(self.empty.lexmax(), Empty)