def test_functions_with_expression(self):
self.assertEqual(str(abs(e_x)), "abs(x)")
self.assertEqual(str(exp(e_x)), "exp(x)")
self.assertEqual(str(sqrt(e_x)), "sqrt(x)")
self.assertEqual(str(pow(e_x, e_y)), "pow(x, y)")
self.assertEqual(str(sin(e_x)), "sin(x)")
self.assertEqual(str(cos(e_x)), "cos(x)")
self.assertEqual(str(tan(e_x)), "tan(x)")
self.assertEqual(str(asin(e_x)), "asin(x)")
self.assertEqual(str(acos(e_x)), "acos(x)")
self.assertEqual(str(atan(e_x)), "atan(x)")
self.assertEqual(str(atan2(e_x, e_y)), "atan2(x, y)")
self.assertEqual(str(sinh(e_x)), "sinh(x)")
self.assertEqual(str(cosh(e_x)), "cosh(x)")
self.assertEqual(str(tanh(e_x)), "tanh(x)")
self.assertEqual(str(min(e_x, e_y)), "min(x, y)")
self.assertEqual(str(max(e_x, e_y)), "max(x, y)")
self.assertEqual(str(if_then_else(e_x > e_y, e_x, e_y)),
"(if (x > y) then x else y)")
def test_functions_with_variable(self):
self.assertEqual(str(abs(x)), "abs(x)")
self.assertEqual(str(exp(x)), "exp(x)")
self.assertEqual(str(sqrt(x)), "sqrt(x)")
self.assertEqual(str(pow(x, y)), "pow(x, y)")
self.assertEqual(str(sin(x)), "sin(x)")
self.assertEqual(str(cos(x)), "cos(x)")
self.assertEqual(str(tan(x)), "tan(x)")
self.assertEqual(str(asin(x)), "asin(x)")
self.assertEqual(str(acos(x)), "acos(x)")
self.assertEqual(str(atan(x)), "atan(x)")
self.assertEqual(str(atan2(x, y)), "atan2(x, y)")
self.assertEqual(str(sinh(x)), "sinh(x)")
self.assertEqual(str(cosh(x)), "cosh(x)")
self.assertEqual(str(tanh(x)), "tanh(x)")
self.assertEqual(str(min(x, y)), "min(x, y)")
self.assertEqual(str(max(x, y)), "max(x, y)")
self.assertEqual(str(if_then_else(x > y, x, y)),
"(if (x > y) then x else y)")
def test_functions_with_float(self):
v_x = 1.0
v_y = 1.0
self.assertEqual(abs(v_x), math.fabs(v_x))
self.assertEqual(exp(v_x), math.exp(v_x))
self.assertEqual(sqrt(v_x), math.sqrt(v_x))
self.assertEqual(pow(v_x, v_y), v_x**v_y)
self.assertEqual(sin(v_x), math.sin(v_x))
self.assertEqual(cos(v_x), math.cos(v_x))
self.assertEqual(tan(v_x), math.tan(v_x))
self.assertEqual(asin(v_x), math.asin(v_x))
self.assertEqual(acos(v_x), math.acos(v_x))
self.assertEqual(atan(v_x), math.atan(v_x))
self.assertEqual(atan2(v_x, v_y), math.atan2(v_x, v_y))
self.assertEqual(sinh(v_x), math.sinh(v_x))
self.assertEqual(cosh(v_x), math.cosh(v_x))
self.assertEqual(tanh(v_x), math.tanh(v_x))
self.assertEqual(min(v_x, v_y), min(v_x, v_y))
self.assertEqual(max(v_x, v_y), max(v_x, v_y))
self.assertEqual(
if_then_else(Expression(v_x) > Expression(v_y), v_x, v_y),
v_x if v_x > v_y else v_y)
print(i, "Lyapunov Risk=", Lyapunov_risk.item())
L.append(Lyapunov_risk.item())
optimizer.zero_grad()
Lyapunov_risk.backward()
optimizer.step()
w1 = model.layer1.weight.data.numpy()
w2 = model.layer2.weight.data.numpy()
b1 = model.layer1.bias.data.numpy()
b2 = model.layer2.bias.data.numpy()
# Falsification
if i % 10 == 0:
f = [x2,
-(system.p.g * dreal.sin(x1) - 2 * system.p.L0 * system.p.delta * x2 ** 3) /
(system.length(vars_) + 2 * system.p.L0 * system.p.delta * x1 * x2)]
# Candidate V
z1 = np.dot(vars_, w1.T) + b1
a1 = []
for j in range(0, len(z1)):
a1.append(dreal.tanh(z1[j]))
z2 = np.dot(a1, w2.T)+b2
V_learn = dreal.tanh(z2.item(0))
print('===========Verifying==========')
start_ = timeit.default_timer()
result= CheckLyapunov(vars_, f, V_learn, ball_lb, ball_ub, config, epsilon)
stop_ = timeit.default_timer()
print(i, "Lyapunov Risk =", Lyapunov_risk.item())
L.append(Lyapunov_risk.item())
optimizer.zero_grad()
Lyapunov_risk.backward()
optimizer.step()
w1 = model.layer1.weight.data.numpy()
w2 = model.layer2.weight.data.numpy()
b1 = model.layer1.bias.data.numpy()
b2 = model.layer2.bias.data.numpy()
# Falsification
if i % 10 == 0:
f = [
x2, -(system.p.g * dreal.sin(x1) +
2 * system.p.L0 * system.p.delta * x2**3) /
(system.length(vars_) + 2 * system.p.L0 * system.p.delta * x1 * x2)
]
# Candidate V
z1 = np.dot(vars_, w1.T) + b1
a1 = []
for j in range(0, len(z1)):
a1.append(dreal.tanh(z1[j]))
z2 = np.dot(a1, w2.T) + b2
V_learn = (z2.item(0))**2
print('===========Verifying==========')
start_ = timeit.default_timer()
def _sympy_converter(var_map, exp, target, expand_pow=False):
rv = None
assert isinstance(exp, sp.Expr) and target is not None
if isinstance(exp, sp.Symbol):
rv = var_map.get(exp.name, None)
elif isinstance(exp, sp.Number):
try:
rv = RealVal(exp) if isinstance(target, Z3Verifier) else sp.RealNumber(exp)
except: # Z3 parser error
rep = sp.Float(exp, len(str(exp)))
rv = RealVal(rep)
elif isinstance(exp, sp.Add):
# Add(exp_0, ...)
rv = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow) # eval this expression
for e in exp.args[1:]: # add it to all other remaining expressions
rv += _sympy_converter(var_map, e, target, expand_pow=expand_pow)
elif isinstance(exp, sp.Mul):
rv = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)
for e in exp.args[1:]:
rv *= _sympy_converter(var_map, e, target, expand_pow=expand_pow)
elif isinstance(exp, sp.Pow):
x = _sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow)
e = _sympy_converter(var_map, exp.args[1], target, expand_pow=expand_pow)
if expand_pow:
try:
i = float(e.sexpr())
assert i.is_integer()
i = int(i) - 1
rv = x
for _ in range(i):
rv *= x
except: # fallback
rv = _sympy_converter(var_map, exp, target, expand_pow=False)
else:
rv = x ** e
elif isinstance(exp, sp.Max):
x = _sympy_converter(var_map, exp.args[1], target, expand_pow=expand_pow)
zero = exp.args[0]
if target == Z3Verifier:
rv = z3.If(x >= 0.0, x, 0.0)
else:
rv = dr.max(x, 0.0)
elif isinstance(exp, sp.Heaviside):
x = _sympy_converter(var_map, exp.args[0], target, expand_pow=False)
if target == Z3Verifier:
rv = z3.If(x > 0.0, 1.0, 0.0)
else:
rv = dr.if_then_else(x>0.0, 1.0, 0.0)
elif isinstance(exp, sp.Function):
# check various activation types ONLY FOR DREAL
if isinstance(exp, sp.tanh):
rv = dr.tanh(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow))
elif isinstance(exp, sp.sin):
rv = dr.sin(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow))
elif isinstance(exp, sp.cos):
rv = dr.cos(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow))
elif isinstance(exp, sp.exp):
rv = dr.exp(_sympy_converter(var_map, exp.args[0], target, expand_pow=expand_pow))
else:
ValueError('Term ' + str(exp) + ' not recognised')
assert rv is not None
return rv
def yt(t, y0, theta0, V, Y):
if -0.001 <= Y <= 0.001: return y0 + V * dreal.sin(theta0) * t
return y0 - V * (dreal.cos(theta0 + Y * t) - dreal.cos(theta0)) / Y
def xt(t, x0, theta0, V, Y):
if -0.001 <= Y <= 0.001: return x0 + V * dreal.cos(theta0) * t
return x0 + V * (dreal.sin(theta0 + Y * t) - dreal.sin(theta0)) / Y
