def compute_alpha(self, problem, expr, ctx):
xs = self._collect_expr_variables(expr)
x_bounds = []
for x in xs:
x_view = problem.variable_view(x)
x_l = x_view.lower_bound()
x_u = x_view.upper_bound()
if x_l is None or x_u is None:
raise ValueError(
'Variables must be bounded: name={}, lb={}, ub={}'.format(
x.name, x_l, x_u))
x_bounds.append(Interval(x_l, x_u))
tree_data = expr.expression_tree_data()
f = tree_data.eval(x_bounds)
H = f.hessian(x_bounds, [1.0])
n = len(xs)
min_ = 0
H = [Interval.zero() + i for i in H]
for i in range(n):
h = H[i * n:(i + 1) * n]
v = h[i].lower_bound - sum(
max(abs(h[j].lower_bound), abs(h[j].upper_bound))
for j in range(n) if j != i)
if v < min_:
min_ = v
alpha = max(0, -0.5 * min_)
return alpha
def bound_description_to_bound(bound_str):
if isinstance(bound_str, str):
return {
'zero': Interval.zero(),
'nonpositive': Interval(None, 0),
'nonnegative': Interval(0, None),
'positive': Interval(1, None),
'negative': Interval(None, -1),
'unbounded': Interval(None, None),
}[bound_str]
elif isinstance(bound_str, Interval):
return bound_str
else:
return Interval(bound_str, bound_str)
def test_addition_with_zero(self, bound):
zero_bound = Interval.zero()
assert bound + zero_bound == bound