def step(self):
self._iteration_k += 1
subgradient = self.state().middle_subgradient()
subgradient_norm = distance.norm(subgradient, ord=2)
t_k = self._step_size_selector.step_size(subgradient_norm,
self._state.score(),
self._iteration_k)
shifted = self.state().x() - t_k * subgradient
projected = l1_projection.project_into_simplex(shifted)
self._state = self.state().move_to_x(projected)
def test_projected_point_is_closer_than_adjacent_points(self):
n = 5
original = np.abs(np.random.randn(n) / n)
projection = l1_projection.project_into_simplex(original)
for i in xrange(n):
adjacent = add_ei(original, i, n)
in_l1_ball = adjacent_point_in_simplex(adjacent)
self.assertLess(distance.euclidean(original, projection),
distance.euclidean(original, in_l1_ball))
def test_projection_point_is_closer_than_adjacent_points_when_point_contains_repeating_values(self):
n = 5
T = 100
for _ in xrange(T):
original = np.random.randn(n) * 0.2 + 2
print original.shape, original
original[2] = original[3] = original[4]
projection = l1_projection.project_into_simplex(original)
for i in xrange(n):
adjacent = add_ei(original, i, n)
in_l1_ball = adjacent_point_in_simplex(adjacent)
self.assertLess(distance.euclidean(original, projection),
distance.euclidean(original, in_l1_ball))
def test_projection_is_identity_for_points_in_the_simplex(self):
for n in xrange(1, 20):
original = np.random.randn(n) * 0.1 + 0.5
in_simplex = adjacent_point_in_simplex(original)
projection = l1_projection.project_into_simplex(in_simplex)
self.assertTrue(np.all(np.isclose(projection, in_simplex)), msg="projection={} in_simplex={}, diff={}".format(projection, in_simplex, projection - in_simplex))
def test_projected_point_is_in_simplex(self):
for n in xrange(1, 20):
original = np.abs(np.random.randn(n) * 0.02 + 1. / n)
projection = l1_projection.project_into_simplex(original)
self.assertTrue(np.all(projection >= 0))
self.assertAlmostEqual(np.sum(projection), 1, delta=0.000001)