def test_basic_composition(self):
x, y = cp.Variable(2)
expr = cp.maximum(cp.ceil(cp.ceil(x)), cp.ceil(cp.ceil(y)))
problem = cp.Problem(cp.Minimize(expr), [x >= 12, x <= 17, y >= 17.4])
self.assertTrue(problem.is_dqcp())
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 18.0)
self.assertLess(x.value, 17.1)
self.assertGreater(x.value, 11.9)
self.assertGreater(y.value, 17.3)
# This problem should have the same solution.
expr = cp.maximum(cp.floor(cp.ceil(x)), cp.floor(cp.ceil(y)))
problem = cp.Problem(cp.Minimize(expr), [x >= 12, x <= 17, y >= 17.4])
self.assertTrue(problem.is_dqcp())
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 18.0)
self.assertLess(x.value, 17.1)
self.assertGreater(x.value, 11.9)
self.assertGreater(y.value, 17.3)
def test_basic_floor(self):
x = cp.Variable()
expr = cp.floor(x)
self.assertTrue(expr.is_dqcp())
self.assertTrue(expr.is_quasiconvex())
self.assertTrue(expr.is_quasiconcave())
self.assertFalse(expr.is_convex())
self.assertFalse(expr.is_concave())
self.assertFalse(expr.is_dcp())
self.assertFalse(expr.is_dgp())
problem = cp.Problem(cp.Minimize(expr), [x >= 11.8, x <= 17])
self.assertTrue(problem.is_dqcp())
self.assertFalse(problem.is_dcp())
self.assertFalse(problem.is_dgp())
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 11.0)
self.assertGreater(x.value, 11.7)