def test_group_lasso_atom():
ps = np.array([0]*5 + [3]*3)
weights = {3:2., 0:2.3}
lagrange = 1.5
lipschitz = 0.2
p = gl.group_lasso(ps, weights=weights, lagrange=lagrange)
z = 30 * np.random.standard_normal(8)
q = rr.identity_quadratic(lipschitz, z, 0, 0)
x = p.solve(q)
a = ml.mixed_lasso_lagrange_prox(z, lagrange, lipschitz,
np.array([],np.int),
np.array([],np.int),
np.array([], np.int),
np.array([], np.int),
np.array([0,0,0,0,0,1,1,1]), np.array([np.sqrt(5), 2]))
result = np.zeros_like(a)
result[:5] = z[:5] / np.linalg.norm(z[:5]) * max(np.linalg.norm(z[:5]) - weights[0] * lagrange/lipschitz, 0)
result[5:] = z[5:] / np.linalg.norm(z[5:]) * max(np.linalg.norm(z[5:]) - weights[3] * lagrange/lipschitz, 0)
lipschitz = 1.
q = rr.identity_quadratic(lipschitz, z, 0, 0)
x2 = p.solve(q)
pc = p.conjugate
a2 = pc.solve(q)
np.testing.assert_allclose(z-a2, x2)
def test_group_lasso_prox():
prox_center = np.array([1,3,5,7,-9,3,4,6,7,8,9,11,13,4,-23,40], np.float)
l1_penalty = np.array([0,1], np.int)
unpenalized = np.array([2,3], np.int)
positive_part = np.array([4,5], np.int)
nonnegative = np.array([], np.int)
groups = np.array([-2,-2,-1,-1,-3,-3] + [0]*5 + [1]*5)
weights = np.array([1.,1.])
lagrange = 1.
lipschitz = 0.5
result = np.zeros_like(prox_center)
result[unpenalized] = prox_center[unpenalized]
result[positive_part] = (prox_center[positive_part] - lagrange / lipschitz) * np.maximum(prox_center[positive_part] - lagrange / lipschitz, 0)
result[l1_penalty] = np.maximum(np.fabs(prox_center[l1_penalty]) - lagrange / lipschitz, 0) * np.sign(prox_center[l1_penalty])
result[6:11] = prox_center[6:11] / np.linalg.norm(prox_center[6:11]) * max(np.linalg.norm(prox_center[6:11]) - weights[0] * lagrange/lipschitz, 0)
result[11:] = prox_center[11:] / np.linalg.norm(prox_center[11:]) * max(np.linalg.norm(prox_center[11:]) - weights[1] * lagrange/lipschitz, 0)
prox_result = ml.mixed_lasso_lagrange_prox(prox_center, lagrange, lipschitz, l1_penalty, unpenalized, positive_part, nonnegative, groups, weights)
np.testing.assert_allclose(result, prox_result)
