def integrate(self, domain: Domain, expression: int, variables=None) -> int:
result = expression
integrator = ResolveIntegrator(
self.pool, reduce_strategy=self.reduce_strategy[1],
)
for v in variables or domain.variables:
result = integrator.integrate(result, domain.get_symbol(v))
return result
def bool_xor_problem():
variables = ["a", "b"]
var_types = {"a": BOOL, "b": BOOL}
var_domains = dict()
domain = Domain(variables, var_types, var_domains)
a, b = (domain.get_symbol(v) for v in variables)
theory = (a & ~b) | (~a & b)
return domain, theory, "2xor"
def ice_cream_problem():
variables = ["chocolate", "banana", "weekend"]
chocolate, banana, weekend = variables
var_types = {chocolate: REAL, banana: REAL, weekend: BOOL}
var_domains = {chocolate: (0, 1), banana: (0, 1)}
domain = Domain(variables, var_types, var_domains)
chocolate, banana, weekend = (domain.get_symbol(v) for v in variables)
theory = (chocolate < 0.650) \
& (banana < 0.550) \
& (chocolate + 0.7 * banana <= 0.700) \
& (chocolate + 1.2 * banana <= 0.750) \
& (~weekend | (chocolate + 0.7 * banana <= 0.340))
return domain, theory, "ice_cream"
def plot_combined(feat_x: Union[str, int],
feat_y: Union[str, int],
domain: Domain,
formula: Optional[FNode],
data: Union[Tuple[np.ndarray, np.ndarray],
List[Tuple[Dict, bool]]],
learned_labels: Optional[List[bool]],
name: str,
active_indices: Set[int],
new_active_indices: Set[int],
condition: Optional[callable] = None):
row_vars = domain.bool_vars[:int(len(domain.bool_vars) / 2)]
col_vars = domain.bool_vars[int(len(domain.bool_vars) / 2):]
sf_size = 2
fig = plt.figure(num=None,
figsize=(2**len(col_vars) * sf_size,
2**len(row_vars) * sf_size),
dpi=300)
for assignment in itertools.product([True, False],
repeat=len(domain.bool_vars)):
row = 0
for b in assignment[:len(row_vars)]:
row = row * 2 + (1 if b else 0)
col = 0
for b in assignment[len(row_vars):]:
col = col * 2 + (1 if b else 0)
index = row * (2**len(col_vars)) + col
ax = fig.add_subplot(2**len(row_vars), 2**len(col_vars), 1 + index)
if formula is not None:
substitution = {
domain.get_symbol(v): smt.Bool(a)
for v, a in zip(domain.bool_vars, assignment)
}
substituted = smt.simplify(formula.substitute(substitution))
try:
region = RegionBuilder(domain).walk_smt(substituted)
try:
if region.dim == 2:
region.linestyle = None
region.plot(ax=ax, color="green", alpha=0.2)
except IndexError:
pass
except ValueError:
pass
points = []
def status(_i):
return "active" if _i in active_indices else (
"new_active" if _i in new_active_indices else "excluded")
if isinstance(data, tuple):
values, labels = data # type: Tuple[np.ndarray, np.ndarray]
var_index_map = domain.var_index_map()
fx, fy = (f if isinstance(f, int) else var_index_map[f]
for f in (feat_x, feat_y))
# noinspection PyUnresolvedReferences
for i in range(values.shape[0]):
row = values[i, :]
point = row[fx], row[fy]
label = labels[i] == 1
correct = (learned_labels[i]
== label) if learned_labels is not None else True
match = all(row[var_index_map[v]] == a
for v, a in zip(domain.bool_vars, assignment))
if match and (condition is None or condition(row, label)):
points.append((label, correct, status(i), point))
else:
for i in range(len(data)):
instance, label = data[i]
point = (float(instance[feat_x]), float(instance[feat_y]))
correct = (learned_labels[i]
== label) if learned_labels is not None else True
match = all(instance[v] == a
for v, a in zip(domain.bool_vars, assignment))
if match and (condition is None or condition(instance, label)):
points.append((label, correct, status(i), point))
def get_color(_l, _c, _s):
if _s == "active":
return "black"
return "green" if _l else "red"
def get_marker(_l, _c, _s):
# if _s == "active":
# return "v"
return "+" if _l else "."
def get_alpha(_l, _c, _s):
if _s == "active":
return 0.5
elif _s == "new_active":
return 1
elif _s == "excluded":
return 0.2
for label in [True, False]:
for correct in [True, False]:
for status in ["active", "new_active", "excluded"]:
marker, color, alpha = [
f(label, correct, status)
for f in (get_marker, get_color, get_alpha)
]
selection = [
p for l, c, s, p in points
if l == label and c == correct and s == status
]
if len(selection) > 0:
ax.scatter(*zip(*selection),
c=color,
marker=marker,
alpha=alpha)
ax.set_xlim(domain.var_domains[feat_x])
ax.set_ylim(domain.var_domains[feat_y])
if name is not None:
plt.savefig(name if name.endswith(".png") else "{}.png".format(name))
else:
plt.show()
plt.close(fig)
def learn_partial(self, solver, domain: Domain, data: np.ndarray,
labels: np.ndarray, new_active_indices: Set):
# Constants
n_b_original = len(domain.bool_vars)
n_b = n_b_original * 2
n_r = len(domain.real_vars)
n_h_original = self.half_space_count if n_r > 0 else 0
n_h = n_h_original * 2 if self.allow_negations else n_h_original
n_c = self.conjunction_count
n_d = data.shape[0]
real_indices = np.array(
[domain.var_types[v] == smt.REAL for v in domain.variables])
real_features = data[:, real_indices]
bool_features = data[:, np.logical_not(real_indices)]
# Variables
a_hr = [[
smt.Symbol("a_hr[{}][{}]".format(h, r), REAL) for r in range(n_r)
] for h in range(n_h_original)]
b_h = [
smt.Symbol("b_h[{}]".format(h), REAL) for h in range(n_h_original)
]
s_ch = [[smt.Symbol("s_ch[{}][{}]".format(c, h)) for h in range(n_h)]
for c in range(n_c)]
s_cb = [[smt.Symbol("s_cb[{}][{}]".format(c, b)) for b in range(n_b)]
for c in range(n_c)]
# Aux variables
s_ih = [[smt.Symbol("s_ih[{}][{}]".format(i, h)) for h in range(n_h)]
for i in range(n_d)]
s_ic = [[smt.Symbol("s_ic[{}][{}]".format(i, c)) for c in range(n_c)]
for i in range(n_d)]
def pair(real: bool, c: int, index: int) -> Tuple[FNode, FNode]:
if real:
return s_ch[c][index], s_ch[c][index + n_h_original]
else:
return s_cb[c][index], s_cb[c][index + n_b_original]
def order_equal(pair1, pair2):
x_t, x_f, y_t, y_f = pair1 + pair2
return smt.Iff(x_t, y_t) & smt.Iff(x_f, y_f)
def order_geq(pair1, pair2):
x_t, x_f, y_t, y_f = pair1 + pair2
return x_t | y_f | ((~x_f) & (~y_t))
def pairs(c: int) -> List[Tuple[FNode, FNode]]:
return [pair(True, c, i) for i in range(n_h_original)
] + [pair(False, c, i) for i in range(n_b_original)]
def order_geq_lex(c1: int, c2: int):
pairs_c1, pairs_c2 = pairs(c1), pairs(c2)
assert len(pairs_c1) == len(pairs_c2)
constraints = smt.TRUE()
for j in range(len(pairs_c1)):
condition = smt.TRUE()
for i in range(j):
condition &= order_equal(pairs_c1[i], pairs_c2[i])
constraints &= smt.Implies(condition,
order_geq(pairs_c1[j], pairs_c2[j]))
return constraints
# Constraints
for i in new_active_indices:
x_r, x_b, label = [float(val) for val in real_features[i]
], bool_features[i], labels[i]
for h in range(n_h_original):
sum_coefficients = smt.Plus(
[a_hr[h][r] * smt.Real(x_r[r]) for r in range(n_r)])
solver.add_assertion(
smt.Iff(s_ih[i][h], sum_coefficients <= b_h[h]))
for h in range(n_h_original, n_h):
solver.add_assertion(
smt.Iff(s_ih[i][h], ~s_ih[i][h - n_h_original]))
for c in range(n_c):
solver.add_assertion(
smt.Iff(
s_ic[i][c],
smt.
Or([smt.FALSE()] + [(s_ch[c][h] & s_ih[i][h])
for h in range(n_h)] +
[s_cb[c][b]
for b in range(n_b_original) if x_b[b]] + [
s_cb[c][b] for b in range(n_b_original, n_b)
if not x_b[b - n_b_original]
])))
# --- [start] symmetry breaking ---
# Mutually exclusive
if "m" in self.symmetries:
for c in range(n_c):
for h in range(n_h_original):
solver.add_assertion(~(s_ch[c][h]
& s_ch[c][h + n_h_original]))
for b in range(n_b_original):
solver.add_assertion(~(s_cb[c][b]
& s_cb[c][b + n_b_original]))
# Normalized
if "n" in self.symmetries:
for h in range(n_h_original):
solver.add_assertion(
smt.Equals(b_h[h], smt.Real(1.0))
| smt.Equals(b_h[h], smt.Real(0.0)))
# Vertical symmetries
if "v" in self.symmetries:
for c in range(n_c - 1):
solver.add_assertion(order_geq_lex(c, c + 1))
# Horizontal symmetries
if "h" in self.symmetries:
for h in range(n_h_original - 1):
solver.add_assertion(a_hr[h][0] >= a_hr[h + 1][0])
# --- [end] symmetry breaking ---
if label:
solver.add_assertion(smt.And([s_ic[i][c] for c in range(n_c)]))
else:
solver.add_assertion(smt.Or([~s_ic[i][c] for c in range(n_c)]))
solver.solve()
model = solver.get_model()
x_vars = [domain.get_symbol(domain.real_vars[r]) for r in range(n_r)]
half_spaces = [
smt.Plus(
[model.get_value(a_hr[h][r]) * x_vars[r]
for r in range(n_r)]) <= model.get_value(b_h[h])
for h in range(n_h_original)
] + [
smt.Plus(
[model.get_value(a_hr[h][r]) * x_vars[r]
for r in range(n_r)]) > model.get_value(b_h[h])
for h in range(n_h - n_h_original)
]
b_vars = [
domain.get_symbol(domain.bool_vars[b]) for b in range(n_b_original)
]
bool_literals = [b_vars[b] for b in range(n_b_original)]
bool_literals += [~b_vars[b] for b in range(n_b - n_b_original)]
conjunctions = [[
half_spaces[h]
for h in range(n_h) if model.get_py_value(s_ch[c][h])
] + [
bool_literals[b]
for b in range(n_b) if model.get_py_value(s_cb[c][b])
] for c in range(n_c)]
return smt.And([smt.Or(conjunction) for conjunction in conjunctions])
