def test_smoothjoin_alpha(self):
a = AbsInterval(torch.tensor([0.0, 1.0]), torch.tensor([5.0, 6.0]), 0.6)
b = AbsInterval(torch.tensor([-2.0, 0.0]), torch.tensor([-1.0, 1.0]), 0.4)
res = AbsInterval.smooth_join([a, b])
print(res)
self.assertEqual(res.alpha, 1.0)
def test_simple_ite(self):
# x in [-1, 5]
x = AbsInterval(torch.tensor([-1.0]), torch.tensor([5.0]), 1.0)
# if x > c
# then x = 2x
# else x = -0.5
program = IfThenElse(
IntervalBool(torch.tensor([1.0]), torch.tensor([0.0])),
AssignStatement(torch.tensor([[2.0]]), torch.tensor([0.0])),
AssignStatement(torch.tensor([[0.0]]), torch.tensor([-0.5])))
# x in [-0.5, 10]
self.assertEqual(
program.propagate(x, t_os),
AbsInterval(torch.tensor([-0.5]), torch.tensor([10.0]), 1.0))
def test_ite_alwaystrue(self):
# x in [-1, 5]
x = AbsInterval(torch.tensor([-1.0]), torch.tensor([5.0]), 1.0)
# if 0x + 3 >= 0
# then x = 2x
# else x = -5
program = IfThenElse(
IntervalBool(torch.tensor([0.0]), torch.tensor([3.0])),
AssignStatement(torch.tensor([[2.0]]), torch.tensor([0.0])),
AssignStatement(torch.tensor([[0.0]]), torch.tensor([-5.0])))
# x in [-2, 10]
self.assertEqual(
program.propagate(x, t_os),
AbsInterval(torch.tensor([-2.0]), torch.tensor([10.0]), 1.0))
def repl(program):
inptL = torch.tensor([-1.0, -1.0])
inptH = torch.tensor([1.0, 1.0])
beta = 1.0
while (True):
cmd = input("> ")
cmds = cmd.split(" ")
if len(cmds) == 3 and cmds[1] == '=':
if cmds[0] == 'xL':
inptL[0] = float(cmds[2])
elif cmds[0] == 'xH':
inptH[0] = float(cmds[2])
elif cmds[0] == 'cL':
inptL[1] = float(cmds[2])
elif cmds[0] == 'cH':
inptH[1] = float(cmds[2])
elif cmds[0] == 'beta':
beta = float(cmds[2])
else:
print("Unknown var")
elif cmd == 'run':
interval = AbsInterval(inptL, inptH, 1.0)
optim_state = OptimizerState(beta=beta,
lambda_const=1 / 2,
smooth=True)
print("Output:")
print(program.propagate(interval, optim_state))
else:
print("Usage:")
print("\tx = v\t x is a name of a variable, v is a value")
print("Variables are xL, xH, cL, cH, beta")
print("\trun\t runs the program")
def propagate(self, A, optim_state):
Lval, Hval = self.E.evaluate(A)
#print("L:%s, H:%s" % (str(Lval), str(Hval)))
L = A.L.clone()
H = A.H.clone()
L[self.i] = Lval
H[self.i] = Hval
return AbsInterval(L, H, A.alpha)
def test_size_decreases_with_alpha(self):
last_width = torch.tensor([0.0, 0.0])
for a in np.arange(0.01, 1.5, 0.02):
# Keep one alpha 1.0, increase the other
v1 = AbsInterval(torch.tensor([2.0, 1.0]), torch.tensor([4.0, 3.0]), 1.0)
v2 = AbsInterval(torch.tensor([-1.0, 0.0]), torch.tensor([5.0, 4.0]), a)
joined = AbsInterval.smooth_join([v1, v2])
hard_joined = v1.join(v2)
# Our interval should get bigger at all iterations
self.assertTrue((joined.H - joined.L >= last_width).all())
# Our interval should be inside a hard join
self.assertTrue((joined.L >= hard_joined.L).all())
self.assertTrue((joined.H <= hard_joined.H).all())
# Our interval should be bigger than the interval with alpha=1.0
self.assertTrue((joined.H >= v1.H).all())
self.assertTrue((joined.L <= v1.L).all())
last_width = joined.H -joined.L
def test_ite_alwaysfalse(self):
# x in [-5, 5]
x = AbsInterval(torch.tensor([-5.0]), torch.tensor([5.0]), 1.0)
# if 2x - 11 >= 0
# then x = 2x
# else x = -5
program = IfThenElse(
IntervalBool(torch.tensor([2.0]), torch.tensor([-11.0])),
AssignStatement(torch.tensor([[2.0]]), torch.tensor([0.0])),
AssignStatement(torch.tensor([[0.0]]), torch.tensor([-5.0])))
# x in [-5, -5]
self.assertEqual(
program.propagate(x, t_os),
AbsInterval(torch.tensor([-5.0]), torch.tensor([-5.0]), 1.0))
# Discontinuity exhibit 1: as input bound increases by 1, output jumps by 17
# x in [-5, 6]
x = AbsInterval(torch.tensor([-5.0]), torch.tensor([6.0]), 1.0)
# x in [-5, 12]
self.assertEqual(
program.propagate(x, t_os),
AbsInterval(torch.tensor([-5.0]), torch.tensor([12.0]), 1.0))
def closure():
optimizer.zero_grad()
optim_state.loss = torch.tensor([0.0], requires_grad=True)
inferred_xL = torch.cat((xL, inferred_paramL), 0)
inferred_xH = torch.cat((xH, inferred_paramH), 0)
interval = AbsInterval(inferred_xL, inferred_xH, 1.0)
#print("in: %s" % (str(interval)))
y = program.propagate(interval, optim_state)
loss = optim_state.loss
loss.backward()
print("b: %f, Loss: %s,\n in: %s, \n out: %s" %
(beta, str(loss.item()), str(interval), str(y)))
return loss
def test_ite_bad_ex(self):
val = AbsInterval(torch.tensor([-10.0, 0.0]),
torch.tensor([1.0, -0.0001]))
program = StatementBlock([
IfThenElse(
IntervalBool(torch.tensor([0.0, 1.0]), torch.tensor([0.0,
0.0])),
AssignStatement(torch.tensor([[2.0, 1.0], [0.0, 1.0]]),
torch.tensor([0.0, 0.0])),
AssignStatement(torch.tensor([[0.0, 0.0], [0.0, 1.0]]),
torch.tensor([700.0, 0.0]))),
ReturnStatement(torch.tensor([1.0, 0.0]), torch.tensor([0.0, 0.0]))
])
def create_interval(inferred_param, xL, xH):
inferred_paramL, inferred_paramH = toWZ(inferred_param)
inferred_paramL, inferred_paramH = torch.tensor(inferred_paramL).type(
torch.FloatTensor), torch.tensor(inferred_paramH).type(
torch.FloatTensor)
inferred_paramL, inferred_paramH = torch.min(
inferred_paramL,
inferred_paramH), torch.max(inferred_paramL, inferred_paramH)
optim_state.loss = torch.tensor([0.0])
inferred_xL = torch.cat((xL, inferred_paramL), 0)
inferred_xH = torch.cat((xH, inferred_paramH), 0)
return AbsInterval(inferred_xL, inferred_xH, 1.0)
def test_simple_ite_full(self):
x1 = AbsInterval(torch.tensor([-10.0, 0.5]), torch.tensor([1.0, 0.5]),
1.0)
x2 = AbsInterval(torch.tensor([-10.0, -0.5]),
torch.tensor([1.0, -0.5]), 1.0)
program = StatementBlock([
IfThenElse(
IntervalBool(torch.tensor([0.0, 1.0]), torch.tensor([0.0,
0.0])),
AssignStatement(torch.tensor([[2.0, -1.0], [0.0, 1.0]]),
torch.tensor([0.0, 0.0])),
AssignStatement(torch.tensor([[0.0, 0.0], [0.0, 1.0]]),
torch.tensor([700.0, 0.0]))),
ReturnStatement(torch.tensor([1.0, 0.0]), torch.tensor([0.0, 0.0]))
])
self.assertEqual(
program.propagate(x1, t_os),
AbsInterval(torch.tensor([-20.5, 0.5]), torch.tensor([1.5, 0.5]),
1.0))
self.assertEqual(
program.propagate(x2, t_os),
AbsInterval(torch.tensor([700.0, -0.5]),
torch.tensor([700.0, -0.5]), 1.0))
def propagate(self, A, optim_state):
L, H = self.expr.evaluate(A)
Ap = AbsInterval(L, H, A.alpha)
optim_state.add_loss(Ap.signed_volume())
return Ap
def test_meet_div0_true(self):
# [1, 5] meet (0x + 1 > 0) -> [1, 5]
val = AbsInterval(torch.tensor([1.0]), torch.tensor([5.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([0.0]), torch.tensor([1.0])), t_os),
AbsInterval(torch.tensor([1.0]), torch.tensor([5.0]), 1.0))
def test_meet_div0_false(self):
# [1, 5] meet (0x - 1 > 0) -> empty
val = AbsInterval(torch.tensor([1.0]), torch.tensor([5.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([0.0]), torch.tensor([-1.0])), t_os),
AbsInterval(torch.tensor([float('inf')]), torch.tensor([float('-inf')]), 0.0))
# ([-1, 5], [1, 3]) meet 0x1 >= 0 and 0x2 - 1 >= 0 => EMPTY
val = AbsInterval(torch.tensor([-1.0, 1.0]), torch.tensor([5.0, 3.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([0.0, 0.0]), torch.tensor([0.0, -1.0])), t_os),
AbsInterval(torch.tensor([float('inf'), float('inf')]), torch.tensor([float('-inf'), float('-inf')]), 0.0))
# ([-1, 5], [1, 3]) meet 0x1 >= 0 and 0x2 + 1 >= 0 => ([-1, 5], [1, 3])
val = AbsInterval(torch.tensor([-1.0, 1.0]), torch.tensor([5.0, 3.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([0.0, 0.0]), torch.tensor([0.0, 1.0])), t_os),
val)
def test_meet_prog(self):
x1 = AbsInterval(torch.tensor([-10.0, 0.5]), torch.tensor([1.0, 0.5]), 1.0)
x2 = AbsInterval(torch.tensor([-10.0, -0.5]), torch.tensor([1.0, -0.5]), 1.0)
x3 = AbsInterval(torch.tensor([-10.0, -0.5]), torch.tensor([1.0, 0.5]), 1.0)
b = IntervalBool(torch.tensor([0.0, 1.0]), torch.tensor([0.0, 0.0]))
self.assertEqual(x1.meet(b, t_os), x1)
self.assertEqual(x2.meet(b, t_os), AbsInterval(torch.tensor([float('inf'), float('inf')]), torch.tensor([float('-inf'), float('-inf')]), 1.0))
self.assertEqual(x3.meet(b, t_os), AbsInterval(torch.tensor([-10.0, 0.0]), torch.tensor([1.0, 0.5]), 1.0))
def test_meet_basic(self):
# [-1, 5] meet x > 0 => [0, 5]
val = AbsInterval(torch.tensor([-1.0]), torch.tensor([5.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([1.0]), torch.tensor([0.0])), t_os),
AbsInterval(torch.tensor([0.0]), torch.tensor([5.0]), 1.0))
# [-1, 5] meet x - 3 > 0 => [3, 5]
val = AbsInterval(torch.tensor([-1.0]), torch.tensor([5.0]), 1.0)
out = val.meet(IntervalBool(torch.tensor([1.0]), torch.tensor([-3.0])), t_os)
self.assertEqual(out.L, torch.tensor([3.0]))
self.assertEqual(out.H, torch.tensor([5.0]))
# [-5, 3] meet 2x + 3 > 0 => [3, 5]
val = AbsInterval(torch.tensor([-5.0]), torch.tensor([3.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([2.0]), torch.tensor([3.0])), t_os),
AbsInterval(torch.tensor([-1.5]), torch.tensor([3.0]), 1.0))
# ([-1, 5], [1, 3]) meet x1 > 0 and x2 < 0 => ([0, 5], [inf, -inf])
val = AbsInterval(torch.tensor([-1.0, 1.0]), torch.tensor([5.0, 3.0]), 1.0)
self.assertEqual(val.meet(IntervalBool(torch.tensor([1.0, -1.0]), torch.tensor([0.0, 0.0])), t_os),
AbsInterval(torch.tensor([float('inf'), float('inf')]), torch.tensor([float('-inf'), float('-inf')]), 0.0))
def test_smooth_join_basic(self):
v1 = AbsInterval(torch.tensor([-1.0, 1.0, 1.0]), torch.tensor([5.0, 3.0, 3.0]), 1.0)
v2 = AbsInterval(torch.tensor([-1.0, 1.0, 1.0]), torch.tensor([5.0, 3.0, 3.0]), 1.0)
self.assertEqual(AbsInterval.smooth_join([v1, v2]),
AbsInterval(torch.tensor([-1.0, 1.0, 1.0]), torch.tensor([5.0, 3.0, 3.0]), 1.0))