tests/test_linear.py

   1 import functools
   2 import unittest
   3
   4 from fractions import Fraction
   5
   6 from pypol.linear import *
   7
   8
   9 try:
  10     import sympy
  11     def _with_sympy(func):
  12         @functools.wraps(func)
  13         def wrapper(self):
  14             return func(self)
  15         return wrapper
  16 except ImportError:
  17     def _with_sympy(func):
  18         @functools.wraps(func)
  19         def wrapper(self):
  20             raise unittest.SkipTest('SymPy is not available')
  21         return wrapper
  22
  23
  24 class TestExpression(unittest.TestCase):
  25
  26     def setUp(self):
  27         self.x = Expression({'x': 1})
  28         self.y = Expression({'y': 1})
  29         self.z = Expression({'z': 1})
  30         self.zero = Expression(constant=0)
  31         self.one = Expression(constant=1)
  32         self.pi = Expression(constant=Fraction(22, 7))
  33         self.expr = self.x - 2*self.y + 3
  34
  35     def test_new_subclass(self):
  36         self.assertIsInstance(self.x, Symbol)
  37         self.assertIsInstance(self.pi, Constant)
  38         self.assertNotIsInstance(self.x + self.pi, Symbol)
  39         self.assertNotIsInstance(self.x + self.pi, Constant)
  40         xx = Expression({'x': 2})
  41         self.assertNotIsInstance(xx, Symbol)
  42
  43     def test_new_types(self):
  44         with self.assertRaises(TypeError):
  45             Expression('x + y', 2)
  46         self.assertEqual(Expression({'x': 2}), Expression({self.x: 2}))
  47         with self.assertRaises(TypeError):
  48             Expression({0: 2})
  49         with self.assertRaises(TypeError):
  50             Expression({'x': '2'})
  51         self.assertEqual(Expression(constant=1), Expression(constant=self.one))
  52         with self.assertRaises(TypeError):
  53             Expression(constant='1')
  54
  55     def test_symbols(self):
  56         self.assertCountEqual(self.x.symbols, ['x'])
  57         self.assertCountEqual(self.pi.symbols, [])
  58         self.assertCountEqual(self.expr.symbols, ['x', 'y'])
  59
  60     def test_dimension(self):
  61         self.assertEqual(self.x.dimension, 1)
  62         self.assertEqual(self.pi.dimension, 0)
  63         self.assertEqual(self.expr.dimension, 2)
  64
  65     def test_coefficient(self):
  66         self.assertEqual(self.expr.coefficient('x'), 1)
  67         self.assertEqual(self.expr.coefficient('y'), -2)
  68         self.assertEqual(self.expr.coefficient(self.y), -2)
  69         self.assertEqual(self.expr.coefficient('z'), 0)
  70         with self.assertRaises(TypeError):
  71             self.expr.coefficient(0)
  72         with self.assertRaises(TypeError):
  73             self.expr.coefficient(self.expr)
  74
  75     def test_getitem(self):
  76         self.assertEqual(self.expr['x'], 1)
  77         self.assertEqual(self.expr['y'], -2)
  78         self.assertEqual(self.expr[self.y], -2)
  79         self.assertEqual(self.expr['z'], 0)
  80         with self.assertRaises(TypeError):
  81             self.expr[0]
  82         with self.assertRaises(TypeError):
  83             self.expr[self.expr]
  84
  85     def test_coefficients(self):
  86         self.assertCountEqual(self.expr.coefficients(), [('x', 1), ('y', -2)])
  87
  88     def test_constant(self):
  89         self.assertEqual(self.x.constant, 0)
  90         self.assertEqual(self.pi.constant, Fraction(22, 7))
  91         self.assertEqual(self.expr.constant, 3)
  92
  93     def test_isconstant(self):
  94         self.assertFalse(self.x.isconstant())
  95         self.assertTrue(self.pi.isconstant())
  96         self.assertFalse(self.expr.isconstant())
  97
  98     def test_values(self):
  99         self.assertCountEqual(self.expr.values(), [1, -2, 3])
 100
 101     def test_issymbol(self):
 102         self.assertTrue(self.x.issymbol())
 103         self.assertFalse(self.pi.issymbol())
 104         self.assertFalse(self.expr.issymbol())
 105
 106     def test_bool(self):
 107         self.assertTrue(self.x)
 108         self.assertFalse(self.zero)
 109         self.assertTrue(self.pi)
 110         self.assertTrue(self.expr)
 111
 112     def test_pos(self):
 113         self.assertEqual(+self.expr, self.expr)
 114
 115     def test_neg(self):
 116         self.assertEqual(-self.expr, -self.x + 2*self.y - 3)
 117
 118     def test_add(self):
 119         self.assertEqual(self.x + Fraction(22, 7), self.x + self.pi)
 120         self.assertEqual(Fraction(22, 7) + self.x, self.x + self.pi)
 121         self.assertEqual(self.x + self.x, 2 * self.x)
 122         self.assertEqual(self.expr + 2*self.y, self.x + 3)
 123
 124     def test_sub(self):
 125         self.assertEqual(self.x - self.x, 0)
 126         self.assertEqual(self.expr - 3, self.x - 2*self.y)
 127         self.assertEqual(0 - self.x, -self.x)
 128
 129     def test_mul(self):
 130         self.assertEqual(self.pi * 7, 22)
 131         self.assertEqual(self.expr * 0, 0)
 132         self.assertEqual(0 * self.expr, 0)
 133         self.assertEqual(self.expr * 2, 2*self.x - 4*self.y + 6)
 134
 135     def test_div(self):
 136         with self.assertRaises(ZeroDivisionError):
 137             self.expr / 0
 138         self.assertEqual(self.expr / 2, self.x / 2 - self.y + Fraction(3, 2))
 139
 140     def test_str(self):
 141         self.assertEqual(str(Expression()), '0')
 142         self.assertEqual(str(self.x), 'x')
 143         self.assertEqual(str(-self.x), '-x')
 144         self.assertEqual(str(self.pi), '22/7')
 145         self.assertEqual(str(self.expr), 'x - 2*y + 3')
 146
 147     def test_repr(self):
 148         self.assertEqual(repr(self.x), "Symbol('x')")
 149         self.assertEqual(repr(self.one), 'Constant(1)')
 150         self.assertEqual(repr(self.pi), 'Constant(22, 7)')
 151         self.assertEqual(repr(self.x + self.one), "Expression('x + 1')")
 152         self.assertEqual(repr(self.expr), "Expression('x - 2*y + 3')")
 153
 154     def test_fromstring(self):
 155         self.assertEqual(Expression.fromstring('x'), self.x)
 156         self.assertEqual(Expression.fromstring('-x'), -self.x)
 157         self.assertEqual(Expression.fromstring('22/7'), self.pi)
 158         self.assertEqual(Expression.fromstring('x - 2y + 3'), self.expr)
 159         self.assertEqual(Expression.fromstring('x - (3-1)y + 3'), self.expr)
 160         self.assertEqual(Expression.fromstring('x - 2*y + 3'), self.expr)
 161
 162     def test_eq(self):
 163         self.assertEqual(self.expr, self.expr)
 164         self.assertNotEqual(self.x, self.y)
 165         self.assertEqual(self.zero, 0)
 166
 167     def test__toint(self):
 168         self.assertEqual((self.x + self.y/2 + self.z/3)._toint(),
 169                 6*self.x + 3*self.y + 2*self.z)
 170
 171     @_with_sympy
 172     def test_fromsympy(self):
 173         sp_x, sp_y = sympy.symbols('x y')
 174         self.assertEqual(Expression.fromsympy(sp_x), self.x)
 175         self.assertEqual(Expression.fromsympy(sympy.Rational(22, 7)), self.pi)
 176         self.assertEqual(Expression.fromsympy(sp_x - 2*sp_y + 3), self.expr)
 177         with self.assertRaises(ValueError):
 178             Expression.fromsympy(sp_x*sp_y)
 179
 180     @_with_sympy
 181     def test_tosympy(self):
 182         sp_x, sp_y = sympy.symbols('x y')
 183         self.assertEqual(self.x.tosympy(), sp_x)
 184         self.assertEqual(self.pi.tosympy(), sympy.Rational(22, 7))
 185         self.assertEqual(self.expr.tosympy(), sp_x - 2*sp_y + 3)
 186
 187
 188 class TestConstant(unittest.TestCase):
 189
 190     def setUp(self):
 191         self.zero = Constant(0)
 192         self.one = Constant(1)
 193         self.pi = Constant(Fraction(22, 7))
 194
 195     @_with_sympy
 196     def test_fromsympy(self):
 197         self.assertEqual(Constant.fromsympy(sympy.Rational(22, 7)), self.pi)
 198         with self.assertRaises(TypeError):
 199             Constant.fromsympy(sympy.Symbol('x'))
 200
 201
 202 class TestSymbol(unittest.TestCase):
 203
 204     def setUp(self):
 205         self.x = Symbol('x')
 206         self.y = Symbol('y')
 207
 208     def test_name(self):
 209         self.assertEqual(self.x.name, 'x')
 210
 211     def test_symbols(self):
 212         self.assertListEqual(list(symbols('x y')), [self.x, self.y])
 213         self.assertListEqual(list(symbols('x,y')), [self.x, self.y])
 214         self.assertListEqual(list(symbols(['x', 'y'])), [self.x, self.y])
 215
 216     @_with_sympy
 217     def test_fromsympy(self):
 218         sp_x = sympy.Symbol('x')
 219         self.assertEqual(Symbol.fromsympy(sp_x), self.x)
 220         with self.assertRaises(TypeError):
 221             Symbol.fromsympy(sympy.Rational(22, 7))
 222         with self.assertRaises(TypeError):
 223             Symbol.fromsympy(2 * sp_x)
 224         with self.assertRaises(TypeError):
 225             Symbol.fromsympy(sp_x*sp_x)
 226
 227
 228 class TestOperators(unittest.TestCase):
 229
 230     pass
 231
 232
 233 class TestPolyhedron(unittest.TestCase):
 234
 235     def setUp(self):
 236         x, y = symbols('x y')
 237         self.square = Polyhedron(inequalities=[x, 1 - x, y, 1 - y])
 238
 239     def test_symbols(self):
 240         self.assertCountEqual(self.square.symbols, ['x', 'y'])
 241
 242     def test_dimension(self):
 243         self.assertEqual(self.square.dimension, 2)
 244
 245     def test_str(self):
 246         self.assertEqual(str(self.square),
 247             'x >= 0, -x + 1 >= 0, y >= 0, -y + 1 >= 0')
 248
 249     def test_repr(self):
 250         self.assertEqual(repr(self.square),
 251             "Polyhedron('x >= 0, -x + 1 >= 0, y >= 0, -y + 1 >= 0')")
 252
 253     def test_fromstring(self):
 254         self.assertEqual(Polyhedron.fromstring('{x >= 0, -x + 1 >= 0, '
 255             'y >= 0, -y + 1 >= 0}'), self.square)
 256
 257     def test_isempty(self):
 258         self.assertFalse(self.square.isempty())
 259
 260     def test_isuniverse(self):
 261         self.assertFalse(self.square.isuniverse())
 262
 263     @unittest.expectedFailure
 264     @_with_sympy
 265     def test_fromsympy(self):
 266         sp_x, sp_y = sympy.symbols('x y')
 267         self.assertEqual(Polyhedron.fromsympy((sp_x >= 0) & (sp_x <= 1) &
 268             (sp_y >= 0) & (sp_y <= 1)), self.square)
 269
 270     @_with_sympy
 271     def test_tosympy(self):
 272         sp_x, sp_y = sympy.symbols('x y')
 273         self.assertEqual(self.square.tosympy(),
 274             sympy.And(-sp_x + 1 >= 0, -sp_y + 1 >= 0, sp_x >= 0, sp_y >= 0))
 275
 276
 277 class TestEmpty:
 278
 279     def test_repr(self):
 280         self.assertEqual(repr(Empty), 'Empty')
 281
 282     def test_isempty(self):
 283         self.assertTrue(Empty.isempty())
 284
 285     def test_isuniverse(self):
 286         self.assertFalse(Empty.isuniverse())
 287
 288
 289 class TestUniverse:
 290
 291     def test_repr(self):
 292         self.assertEqual(repr(Universe), 'Universe')
 293
 294     def test_isempty(self):
 295         self.assertTrue(Universe.isempty())
 296
 297     def test_isuniverse(self):
 298         self.assertTrue(Universe.isuniverse())