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
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/>.
18 import unittest
20 from ..domains import And, Or
21 from ..linexprs import Symbol, symbols
22 from ..polyhedra import Empty, Eq, Ge, Polyhedron
25 class TestDomain(unittest.TestCase):
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))
61 def test_new(self):
62 with self.assertRaises(TypeError):
63 Polyhedron(1)
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)
70 def test_isempty(self):
71 self.assertFalse(self.square1.isempty())
72 self.assertTrue(self.empty.isempty())
73 self.assertFalse(self.universe.isempty())
75 def test_isuniverse(self):
76 self.assertFalse(self.square1.isuniverse())
77 self.assertTrue(self.universe.isuniverse())
79 def test_isbounded(self):
80 self.assertTrue(self.square1.isbounded())
81 self.assertFalse(self.unbound_poly.isbounded())
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)
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))
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))
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)
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)
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)
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)
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)
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(), {})
135 def test_intersection(self):
136 self.assertEqual(self.square1.intersection(self.square2),
137 self.intersection)
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)
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)
154 def test_or(self):
155 self.assertEqual(self.square1 | self.square2, self.union)
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)
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)
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)
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)