def test_inequality(self):
# Boolean Variable != Boolean Variable
self.assertEqual(b1 != b2, Not(Iff(b1, b2)))
# Boolean Variable != Formula
self.assertEqual(b1 != (x > 3), Not(Iff(b1, x > 3)))
# Formula != Boolean Variable
self.assertEqual((x > 3) != b1, Not(Iff(x > 3, b1)))
# Scalar Variable != Scalar Variable
self.assertEqual(str(x != y), '(x != y)')
# Scalar Variable != Expression
self.assertEqual(str(x != (y + 3)), '(x != (3 + y))')
# Expression != Scalar Variable
self.assertEqual(str((3 + y) != x), '((3 + y) != x)')
# Expression != Expression
self.assertEqual(str((1 + x) != (2 + y)), '((1 + x) != (2 + y))')
def test_logical(self):
f1 = (x == 0)
f2 = (y == 0)
self.assertEqual(str(Not(f1)), "!((x == 0))")
self.assertEqual(str(Implies(f1, f2)), str(Or(Not(f1), f2)))
self.assertEqual(str(Iff(f1, f2)),
str(And(Implies(f1, f2), Implies(f2, f1))))
# Test single-operand logical statements
self.assertEqual(str(And(x >= 1)), "(x >= 1)")
self.assertEqual(str(Or(x >= 1)), "(x >= 1)")
# Test binary operand logical statements
self.assertEqual(str(And(x >= 1, x <= 2)), "((x >= 1) and (x <= 2))")
self.assertEqual(str(Or(x <= 1, x >= 2)), "((x >= 2) or (x <= 1))")
# Test multiple operand logical statements
self.assertEqual(str(And(x >= 1, x <= 2, y == 2)),
"((y == 2) and (x >= 1) and (x <= 2))")
self.assertEqual(str(Or(x >= 1, x <= 2, y == 2)),
"((y == 2) or (x >= 1) or (x <= 2))")
def dReal_check(barrier,
vector_field,
region=TUNCALI_PHASE_U,
exclude=TUNCALI_PHASE_X0):
final_conjuncts = [
region.formula(delta=EPSILON, strict=True),
Not(exclude.formula(strict=True))
]
# Check that there are feasible points in this region
sanity = CheckSatisfiability(And(*final_conjuncts), EPSILON)
if sanity is None:
raise RuntimeError("empty satisfiability region")
# ... and that having negative Lie derivative is required.
ld = barrier.lie_derivative(vector_field, region.variables, mp=DREAL)
final_conjuncts.append(ld > -EPSILON)
result = CheckSatisfiability(And(*final_conjuncts), EPSILON)
return result # should be None
def test_logical2(self):
self.assertEqual(str(And(b1, b2, Implies(b1, b2))),
"(b1 and b2 and (b2 or !(b1)))")
self.assertEqual(str(Or(b1, b2, Implies(b1, b2))),
"(b1 or b2 or !(b1))")
self.assertEqual(str(Not(b1)), "!(b1)")