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 *
  21 from ..linexprs import Symbol, symbols
  22 from ..polyhedra import *
  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]) #correct representation
  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], inequalities=[x - 1, 3 - x, y - 1])
  35         self.unbound_poly = Polyhedron(inequalities=[x, 3 - x, y])
  36         self.universe = Polyhedron([])
  37         self.empty = Empty
  38         self.disjoint = And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
  39         self.complement = Or(Ge(-x - 1, 0), Ge(x - 3, 0), And(Ge(x, 0), Ge(-x + 2, 0), Ge(-y - 1, 0)), And(Ge(x, 0), Ge(-x + 2, 0), Ge(y - 3, 0)))
  40         self.hull = And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
  41         self.dropped = And(Ge(y, 0), Ge(-y + 2, 0))
  42         self.intersection = And(Ge(x - 1, 0), Ge(-x + 2, 0), Ge(y - 1, 0), Ge(-y + 2, 0))
  43         self.union = Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)))
  44         self.sum1 = Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)))
  45         self.sum2 =And(Ge(x, 0), Ge(y, 0), Ge(-y + 3, 0), Ge(-x + 3, 0), Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
  46         self.difference1 = Or(And(Eq(x - 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)), And(Eq(y - 3, 0), Ge(x - 1, 0), Ge(-x + 2, 0)))
  47         self.difference2 = And(Ge(x + y - 4, 0), Ge(-x + 3, 0), Ge(-y + 3, 0))
  48         self.lexmin = And(Eq(y, 0), Eq(x, 0))
  49         self.lexmax = And(Eq(y - 2, 0), Eq(x - 2, 0))
  50
  51     def test_new(self):
  52         with self.assertRaises(TypeError):
  53             Polyhedron(1)
  54
  55     def test_disjoint(self):
  56         self.assertEqual(self.square1.disjoint(), self.disjoint)
  57         self.assertEqual(self.empty.disjoint(), Empty)
  58         self.assertEqual(self.universe.disjoint(), self.universe)
  59
  60     def test_isempty(self):
  61         self.assertFalse(self.square1.isempty())
  62         self.assertTrue(self.empty.isempty())
  63         self.assertFalse(self.universe.isempty())
  64
  65     def test_isuniverse(self):
  66         self.assertFalse(self.square1.isuniverse())
  67         self.assertTrue(self.universe.isuniverse())
  68
  69     def test_isbounded(self):
  70         self.assertTrue(self.square1.isbounded())
  71         self.assertFalse(self.unbound_poly.isbounded())
  72
  73     def test_eq(self):
  74         self.assertTrue(self.square1 == self.square1)
  75         self.assertFalse(self.square1 == self.square2)
  76         self.assertFalse(self.empty == self.universe)
  77
  78     def test_isdisjoint(self):
  79         self.assertFalse(self.square1.isdisjoint(self.square2))
  80         self.assertFalse(self.universe.isdisjoint(self.square1))
  81         self.assertTrue(self.square1.isdisjoint(self.square5))
  82         self.assertTrue(self.empty.isdisjoint(self.square1))
  83
  84     def test_issubset(self):
  85         self.assertTrue(self.square4.issubset(self.unbound_poly))
  86         self.assertFalse(self.square1.issubset(self.square2))
  87         self.assertTrue(self.square1.issubset(self.universe))
  88         self.assertTrue(self.empty.issubset(self.square1))
  89
  90     def test_le(self):
  91         self.assertTrue(self.square4 <= self.square3)
  92         self.assertFalse(self.square3 <= self.square4)
  93         self.assertTrue(self.empty <= self.square1)
  94         self.assertTrue(self.square1 <= self.universe)
  95
  96     def test_lt(self):
  97         self.assertTrue(self.square4 < self.square3)
  98         self.assertFalse(self.square3 < self.square4)
  99         self.assertTrue(self.empty < self.square1)
 100         self.assertTrue(self.square1 < self.universe)
 101
 102     def test_complement(self):
 103         self.assertEqual(~self.square1, self.complement)
 104         self.assertEqual(~self.universe, Empty)
 105         self.assertEqual(~self.empty, self.universe)
 106
 107     def test_aspolyhedron(self):
 108         self.assertEqual(self.square1.aspolyhedron(), self.hull)
 109         self.assertEqual(self.universe.aspolyhedron(), self.universe)
 110         self.assertEqual(self.empty.aspolyhedron(), self.empty)
 111
 112     def test_project(self):
 113         self.assertEqual(self.square1.project(symbols('x')), self.dropped)
 114         self.assertEqual(self.square1.project(symbols('x y')), self.universe)
 115         self.assertEqual(self.universe.project([]), self.universe)
 116         self.assertEqual(self.empty.project([]), Empty)
 117
 118     def test_simplify(self):
 119         self.assertEqual(self.universe.simplify(), self.universe)
 120         self.assertEqual(self.empty.simplify(), Empty)
 121
 122     def test_sample(self):
 123         self.assertEqual(self.square6.sample(), {Symbol('x'): 1, Symbol('y'): 3})
 124         with self.assertRaises(ValueError):
 125             self.empty.sample()
 126         self.assertEqual(self.universe.sample(), {})
 127
 128     def test_intersection(self):
 129         self.assertEqual(self.square1.intersection(self.square2), self.intersection)
 130
 131     def test_and(self):
 132         self.assertEqual(self.square2 & self.square1, self.intersection)
 133         self.assertEqual(self.square1 & self.universe, self.square1)
 134         self.assertEqual(self.empty & self.square1, Empty)
 135         self.assertEqual(self.universe & self.universe, self.universe)
 136         self.assertEqual(self.universe & self.empty, Empty)
 137         self.assertEqual(self.empty & self.empty, Empty)
 138
 139     def test_union(self):
 140         self.assertEqual(self.square1.union(self.square2), self.union)
 141         self.assertEqual(self.square1.union(self.empty), self.square1)
 142         self.assertEqual(self.square1.union(self.universe), self.universe)
 143         self.assertEqual(self.universe.union(self.universe), self.universe)
 144         self.assertEqual(self.empty.union(self.empty), self.empty)
 145
 146     def test_or(self):
 147         self.assertEqual(self.square1 | self.square2, self.union)
 148
 149     def test_add(self):
 150         self.assertEqual(self.square2 + self.square1, self.sum1)
 151         self.assertEqual(Polyhedron(self.square1 + self.square2), self.sum2)
 152         self.assertEqual(self.universe + self.square1, self.universe)
 153         self.assertEqual(self.empty + self.square1, self.square1)
 154         self.assertEqual(self.universe + self.universe, self.universe)
 155
 156     def test_difference(self):
 157         self.assertEqual(self.square2 - self.square1, self.difference1)
 158         self.assertEqual(Polyhedron(self.square2 - self.square1), self.difference2)
 159         self.assertEqual(self.square2 - self.square2, Empty)
 160         self.assertEqual(self.universe - self.universe, Empty)
 161
 162     def test_lexmin(self):
 163         self.assertEqual(self.square1.lexmin(), self.lexmin)
 164         self.assertEqual(self.universe.lexmin(), self.universe)
 165         self.assertEqual(self.empty.lexmin(), Empty)
 166
 167     def test_lexmax(self):
 168         self.assertEqual(self.square1.lexmax(), self.lexmax)
 169         self.assertEqual(self.universe.lexmax(), self.universe)
 170         self.assertEqual(self.empty.lexmax(), Empty)
 171
 172     def test_involves_vars(self):
 173         self.assertTrue(self.square1.involves_vars(symbols('x y')))
 174         self.assertFalse(self.empty.involves_vars(symbols('x')))
 175         self.assertFalse(self.universe.involves_vars(symbols('x')))