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implement error bounds in smooth robustness

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This commit is contained in:
Marcell Vazquez-Chanlatte 2016-12-10 13:59:06 -08:00
parent 8b267fa2c3
commit f5b23637af
1 changed files with 22 additions and 15 deletions
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37
stl/smooth_robustness.py
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@ -11,29 +11,34 @@ from stl.ast import t_sym
from stl.robustness import op_lookup
@singledispatch
def smooth_robustness(stl, L, h):
def smooth_robustness(stl, L, h, eps):
raise NotImplementedError
@smooth_robustness.register(stl.And)
@smooth_robustness.register(stl.G)
def _(stl, L, H):
def _(stl, L, H, eps):
raise NotImplementedError("Call canonicalization function")
def eps_to_base(eps, N):
return N**(1/eps)
def soft_max(rs, eps=0.1):
B = 10
N = len(rs)
B = eps_to_base(eps, N)
return sym.log(sum(B**r for r in rs), B)
def LSE(rs, eps=0.1):
B = 10
return soft_max(rs) - sym.log(len(rs), B)
N = len(rs)
B = eps_to_base(eps, N)
return soft_max(rs) - sym.log(N, B)
@smooth_robustness.register(stl.Or)
def _(stl, L, h):
def _(stl, L, h, eps):
rl, rh = list(zip(
*[smooth_robustness(arg, L, h) for arg in stl.args]))
return soft_max(rl), LSE(rh)
*[smooth_robustness(arg, L, h, eps=eps/2) for arg in stl.args]))
return soft_max(rl, eps=eps/2), LSE(rh, eps=eps/2)
@autocurry
@ -43,22 +48,24 @@ def x_ij(L, h, xi_xj):
@smooth_robustness.register(stl.F)
def _(stl, L, H):
def _(stl, L, H, eps):
lo, hi = stl.interval
times = arange(lo, hi, H)
rl, rh = smooth_robustness(stl.arg, L, H)
los, his = zip(*[(rl.subs({t_sym: t_sym + t}), rh.subs({t_sym: t_sym + t})) for t in times])
return LSE(los), soft_max(map(x_ij(L, H), pairwise(his)))
rl, rh = smooth_robustness(stl.arg, L, H, eps=eps/2)
los, his = zip(*[(rl.subs({t_sym: t_sym + t}),
rh.subs({t_sym: t_sym + t})) for t in times])
x_stars = list(map(x_ij(L, H), pairwise(his)))
return LSE(los, eps=eps/2), soft_max(x_stars, eps=eps/2)
@smooth_robustness.register(stl.Neg)
def _(stl, L, H):
rl, rh = smooth_robustness(arg, L, H)
def _(stl, L, H, eps):
rl, rh = smooth_robustness(arg, L, H, eps)
return -rh, -rl
@smooth_robustness.register(stl.LinEq)
def _(stl, L, H):
def _(stl, L, H, eps):
op = op_lookup[stl.op]
retval = op(eval_terms(stl), stl.const)
return retval, retval