def test_tv1_prox():
"""
Use the properties of strongly convex functions to test the implementation
of the TV1D proximal operator. In particular, we use the following inequality
applied to the proximal objective function: if f is mu-strongly convex then
f(x) - f(x^*) >= ||x - x^*||^2 / (2 mu)
where x^* is the optimum of f.
"""
n_features = 10
gamma = np.random.rand()
epsilon = 1e-10 # account for some numerical errors
tv_norm = lambda x: np.sum(np.abs(np.diff(x)))
for _ in range(1000):
x = np.random.randn(n_features)
x_next = tv_prox.prox_tv1d(x, gamma)
diff_obj = tv_norm(x) - tv_norm(x_next)
testing.assert_array_less(((x - x_next)**2).sum() / gamma,
(1 + epsilon) * diff_obj)
def prox(self, x, step_size):
# imported here to avoid circular imports
from copt import tv_prox
return tv_prox.prox_tv1d(x, step_size * self.alpha)