implemented smooth_robustness for constant base

stl/smooth_robustness.py

@@ -1,88 +1,120 @@
 # TODO: technically incorrect on 0 robustness since conflates < and >
 
 from functools import singledispatch
+from collections import namedtuple
 
 import sympy as sym
 from numpy import arange
 from funcy import pairwise
+from lenses import lens
 
 import stl.ast
 from stl.ast import t_sym
+from stl.utils import walk
 from stl.robustness import op_lookup
 
+Param = namedtuple("Param", ["L", "h", "B", "id_map"])
+
 @singledispatch
-def smooth_robustness(stl, L, h, eps, depth):
-    raise NotImplementedError
-
-@smooth_robustness.register(stl.And)
-@smooth_robustness.register(stl.G)
-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):
-    N = len(rs)
-    B = eps_to_base(eps, N)
-    return sym.log(sum(B**r for r in rs), B)
+def node_base(_, _1, _2):
+    return sym.e
 
 
-def LSE(rs, eps=0.1):
-    N = len(rs)
-    B = eps_to_base(eps, N)
-    return soft_max(rs) - sym.log(N, B)
+@node_base.register(stl.ast.Or)
+def node_base(_, eps, _1):
+    return len(stl.args)**(1/eps)
 
 
-@smooth_robustness.register(stl.Or)
-def _(stl, L, h, eps, depth=0):
-    rl, rh = list(zip(
-        *[smooth_robustness(arg, L, h, eps=eps/2, depth=depth+1)
-          for arg in stl.args]))
-    return soft_max(rl, eps=eps/2), LSE(rh, eps=eps/2)
-
-
-def soft_max2(r, eps, lo, hi, L, H, depth):
-    N = sym.ceiling((hi - lo) / H)
-    B = eps_to_base(eps, N)
-    i = sym.Symbol("i_{}".format(depth))
-    x_ij = (L*H + r.subs({t_sym: t_sym+i}) + r.subs({t_sym: t_sym+i+1}))/2
-    return sym.log(sym.summation(B**x_ij, (i, lo, hi)), B)
-
-def LSE2(r, eps, lo, hi, H, depth):
-    N = sym.ceiling((hi - lo) / H)
-    B = eps_to_base(eps, N)
-    i = sym.Symbol("i_{}".format(depth))
-    x_i = r.subs({t_sym: t_sym+i})
-    return sym.log(sym.summation(B**x_i, (i, lo, hi))/N, B)
-
-
-
-@smooth_robustness.register(stl.F)
-def _(stl, L, H, eps, depth=0):
+@node_base.register(stl.ast.F)
+def node_base(_, eps, L):
     lo, hi = stl.interval
-    times = arange(lo, hi, H)
-    rl, rh = smooth_robustness(stl.arg, L, H, eps=eps/2, depth=depth+1)
-    return (LSE2(rl, eps/2, lo, hi, H, depth), 
-            soft_max2(rh, eps/2, lo, hi, L, H, depth))
+    return sym.ceil((hi - lo)*L/eps)**(2/eps)
 
 
-@smooth_robustness.register(stl.Neg)
-def _(stl, L, H, eps, depth=0):
-    rl, rh = smooth_robustness(arg, L, H, eps, depth=depth+1)
-    return -rh, -rl
+def sample_rate(eps, L):
+    return eps / L
 
 
-@smooth_robustness.register(stl.LinEq)
-def _(stl, L, H, eps, depth=0):
-    op = op_lookup[stl.op]
-    retval = op(eval_terms(stl), stl.const)
-    return retval, retval
+def admissible_params(phi, eps, L):
+    return Param(
+        L=L,
+        h=sample_rate(eps, L),
+        B=max(node_base(n, eps, L) for n in walk(phi)),
+        id_map={n:i for i, n in enumerate(walk(phi))}
+    )
 
 
+def smooth_robustness(phi, eps, L):
+    p = admissible_params(phi, eps, L)
+    lo, hi = beta(phi, p), alpha(phi, p)
+    return sym.log(lo, B), sym.log(hi, B)
+
+
+# Alpha implementation
+
+@singledispatch
+def alpha(stl, p):
+    raise NotImplementedError("Call canonicalization function")
+
 def eval_terms(lineq):
     return sum(map(eval_term, lineq.terms))
 
 
 def eval_term(term):
     return term.coeff*sym.Function(term.id.name)(t_sym)
+
+
+@alpha.register(stl.LinEq)
+def _(phi, p):
+    op = op_lookup[phi.op]
+    B = eps_to_base(eps/depth, N)
+    x = op(eval_terms(phi), phi.const)
+    return B**x
+
+
+@alpha.register(stl.Neg)
+def _(phi, p):
+    return 1/beta(phi, p)
+
+
+@alpha.register(stl.Or)
+def _(phi, p):
+    return sum(alpha(psi, p) for psi in psi in phi.args)
+
+
+def F_params(phi, p, r):
+    hi, lo = phi.interval
+    N = sym.ceiling((hi - lo) / p.h)
+    i = sym.Symbol("i_{}".format(p.id_map[phi]))
+    x = lambda k: r.subs({t_sym: t_sym+k+lo})
+    return N, i, x
+
+
+@alpha.register(stl.F)
+def _(phi, p):
+    N, i, x = F_params(phi, p, alpha(phi.arg, p))
+    x_ij = sym.sqrt(p.B**(L*h)*x(i)*x(i+1))
+    return sym.summation(x_ij, (i, 0, N-1))
+
+# Beta implementation
+
+@singledispatch
+def beta(phi, p):
+    raise NotImplementedError("Call canonicalization function")
+
+beta.register(stl.LinEq)(alpha)
+
+@beta.register(stl.Neg)
+def _(phi, p):
+    return 1/alpha(phi, p)
+
+
+@beta.register(stl.Or)
+def _(phi, p):
+    return alpha(phi)/len(phi.args)
+
+
+@beta.register(stl.F)
+def _(phi, p):
+    N, i, x = F_params(phi, p, beta(phi.arg, p))
+    return sym.summation(x(i), (i, 0, N))